137 results
Search Results
2. Local automorphisms of real B(X).
- Author
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Rakhimov, Abdugafur Abdumadjidovich and Nazarov, Khasanbek Avazbekogli
- Subjects
BANACH spaces ,AUTOMORPHISMS ,LINEAR operators ,ALGEBRA - Abstract
In the paper local and 2-local *-automorphisms on real algebra B(X) of all bounded linear operators on a real Banach space are considered. In particular, 2-local *-automorphisms of real W*-algebra B(H
r ) is described. Namely, it is proved that on real W*-algebra B(Hr ) each *-automorphism is an inner and any 2-local *-automorphism is a *-automorphism. Moreover, it is proved that if X is a real Banach spaces and θ : B(X)→B(X) is a local automorphism, then θ is an automorphism. [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
3. Inner ideals of the special linear lie algebras of associative simple finite dimensional algebras.
- Author
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Shlaka, Hasan M. and Mousa, Durgham A.
- Subjects
ASSOCIATIVE algebras ,LIE algebras ,ALGEBRA ,FINITE, The ,IDEMPOTENTS ,IDEALS (Algebra) - Abstract
In this paper, we discuss and study the structure of inner ideals of the special linear Lie algebras of associative simple algebras. We prove that if A is an associative finite dimensional simple algebra over algebraically closed fields of positive characteristic, then every inner ideal of regular type of [A, A] is generated by a pair of idempotents. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
4. On state space of measurable function in symmetric Δ-Banach algebra with new results.
- Author
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Hussein, Boushra Y. and Wshayeh, Huda A. A.
- Subjects
FUNCTION spaces ,SYMMETRIC functions ,BANACH algebras ,ALGEBRA ,BANACH spaces - Abstract
The aim of this paper is to present new results obtained in the study of spaces with a Δ-symmetric Banach Algebra, we defined the δ-characters functional and discuss the space of measurable function(L
o (µ)) is Δ- symmetric and is Banach algebra. Also, we define sℂ (Lo (µ)) by depended on Lo (µ) and proved the spaces is satisfies new properties in symmetric Banach algebra and prove any function in sℂ (Lo (µ)) satisfies all conditions of state functional and found corresponding between the space sℂ (Lo (µ)) and the space of all o- characters functional δch(Lo (µ)) on Lo (µ) as well as well defined. Also, we proved the functional ψ from Æ into sℂ (Lo (µ)) is continuous and state functional if every non-zero element has an inverse. We proved the quotient sℂ (Lo (µ))/Ι is also symmetric Δ –Banach algebra. [ABSTRACT FROM AUTHOR]- Published
- 2022
- Full Text
- View/download PDF
5. Fuzzy relational equations - Min-Goguen implication.
- Author
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Zahariev, Zlatko, Zaharieva, Galina, and Peeva, Ketty
- Subjects
FUZZY relational equations ,LINEAR systems ,LINEAR equations ,FUZZY systems ,ALGEBRA - Abstract
An algorithm for solving Min-Goguen fuzzy linear systems of equations is presented in this paper. Solving linear systems of equations is subject of great scientific interest. The authors have developed fast an efficient algorithms over several algebras. Here we present, relatively simple, fast and efficient algorithm to solve fuzzy linear systems of equations for Min-Goguen algebra, logically backed by previously developed by the authors algorithms in max-min and min-max algebras. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
6. The idempotency in the genetic algebras generated by QSO on infinite state space.
- Author
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Ftameh, Khaled, Rozali, Wan Nur Fairuz Alwani Bt W., and Hee, Pah Chin
- Subjects
- *
ALGEBRA , *GEOMETRIC distribution , *POISSON distribution - Abstract
In this paper, we recall the notion of a quadratic stochastic operator (QSO) generated by a special distribution on infinite state space. Also, we consider the concept of genetic algebras generated by these QSOs. This paper aims to study the idempotency in the genetic algebras generated by QSO and defined by special distributions, including geometric, Poisson, mixture geometric, mixture Poisson and heterogeneous mixture geometric and Poisson distributions. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
7. Complete classification of two-dimensional algebras over any basic field.
- Author
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Bekbaev, Ural
- Subjects
ALGEBRA ,MATRICES (Mathematics) ,ISOMORPHISM (Mathematics) ,CLASSIFICATION - Abstract
This paper is about the classification, up to isomorphism, of two-dimensional algebras over any basic field. It provides a full classification of such algebras in terms of their matrices of structure constants which is helpful in solving many other problems related to two-dimensional algebras. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
8. Students' mathematical proving ability in the implementation of local instructions theory of learning algebra proofs.
- Author
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Agustiani, Riza, Nursalim, Rahmat, Fitrianti, Yuli, and Arifin, Sujinal
- Subjects
MATHEMATICAL ability ,PHILOSOPHY of education ,ALGEBRA ,MATHEMATICS students ,MATHEMATICS education ,WORD problems (Mathematics) - Abstract
Proof is important in mathematics both as a component of mathematics and as a mathematics learning tool. The ability to construct proof is one indicator of mathematical reasoning, which is a critical component of mathematics learning outcomes, particularly in Algebra. This research aims to describe the students' mathematical proving ability. This design research consists of three stages: preparing for the experiment, the design experiment, and the retrospective analysis. Focus discussion of this paper is only students' mathematical proving ability in the design experiment and the retrospective analysis. This research involved 9 students of mathematics education. The test (post-test) was conducted to collect data about students' mathematical proving ability. This research resulted in a Local Instruction Theory (LIT) of learning algebra proofs which contains 4 activities: reading proof, completing proof, examining proof, and constructing the proof. In the experiment activities, students experienced the common errors, such as assuming the conclusion to prove the conclusion, proving general statements using specific examples, not proving both conditions in a bi conditional statement, and misusing definitions. The common errors Student errors are reduced after all activities are completed. The result of this research showed that mathematical proving ability can be categorized into three score categories, low, middle, and high level. From 9 students involved in this research: 2 students in high level and 7 students in low level or 2 students in high score category, 5 students in middle score category, and 1 student in low score category. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
9. A new approach to G-metric spaces: Algebra G-fuzzy metric spaces.
- Author
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Mohammedali, Mayada N.
- Subjects
METRIC spaces ,ALGEBRA ,SET theory ,FUZZY logic ,FUZZY sets ,FUZZY mathematics - Abstract
Fuzzy mathematics is an area of mathematics concerned with fuzzy set theory and fuzzy logic. The description provided by fuzzy sets is more accurate than the description provided by conventional sets. The paper highlights a bunch of new fuzzy mathematics approaches. The structure of Algebra G-fuzzy metric space (AGFM-space) was introduced, a new type for the concept of G-fuzzy metric space, gives a consistent extension of G-metric space, and leads to further investigations and applications. A condition was proposed for a G*-convergence sequence in the suggested area to be G*-Cauchy. Moreover, some enhanced versions of theoretical applications in AGFM-spaces are developed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
10. Isoclinism and factor set in regular Hom-Lie superalgebras.
- Author
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Nandi, N., Padhan, R. N., and Pati, K. C.
- Subjects
SUPERALGEBRAS ,LIE superalgebras ,ALGEBRA - Abstract
Hom-Lie superalgebras can be considered as the deformation of Lie superalgebras; which are ℤ
2 -graded generalization of Hom-Lie algebras. The motivation of this paper is to introduce the concept of isoclinism and factor set in regular Hom-Lie superalgebras. Finally, we obtain that two finite same dimensional regular Hom-Lie superalgebras are isoclinic if and only if they are isomorphic. [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
11. Topological spectral bands with frieze groups.
- Author
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Lux, Fabian R., Stoiber, Tom, Wang, Shaoyun, Huang, Guoliang, and Prodan, Emil
- Subjects
- *
SEED harvesting , *K-theory , *EXPOSITION (Rhetoric) , *RESONATORS , *ALGEBRA - Abstract
Frieze groups are discrete subgroups of the full group of isometries of a flat strip. We investigate here the dynamics of specific architected materials generated by acting with a frieze group on a collection of self-coupling seed resonators. We demonstrate that, under unrestricted reconfigurations of the internal structures of the seed resonators, the dynamical matrices of the materials generate the full self-adjoint sector of the stabilized group C*-algebra of the frieze group. As a consequence, in applications where the positions, orientations and internal structures of the seed resonators are adiabatically modified, the spectral bands of the dynamical matrices carry a complete set of topological invariants that are fully accounted by the K-theory of the mentioned algebra. By resolving the generators of the K-theory, we produce the model dynamical matrices that carry the elementary topological charges, which we implement with systems of plate resonators to showcase several applications in spectral engineering. The paper is written in an expository style. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
12. Eigenvalues of quantum Gelfand invariants.
- Author
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Jing, Naihuan, Liu, Ming, and Molev, Alexander
- Subjects
- *
QUANTUM groups , *EIGENVALUES , *HECKE algebras , *ALGEBRA - Abstract
We consider the quantum Gelfand invariants which first appeared in a landmark paper by Reshetikhin et al. [Algebra Anal. 1(1), 178–206 (1989)]. We calculate the eigenvalues of the invariants acting in irreducible highest weight representations of the quantized enveloping algebra for g l n . The calculation is based on Liouville-type formulas relating two families of central elements in the quantum affine algebras of type A. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
13. Bases for infinite dimensional simple osp(1|2n)-modules respecting the branching osp(1|2n)⊃gl(n).
- Author
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Bisbo, Asmus K. and Van der Jeugt, Joris
- Subjects
BRANCHING processes ,POLYNOMIALS ,RESPECT ,ALGEBRA ,INTEGERS ,PROJECTORS ,LIE superalgebras - Abstract
We study the effects of the branching o s p (1 | 2 n) ⊃ g l (n) on a particular class of simple infinite-dimensional o s p (1 | 2 n) -modules L(p) characterized by a positive integer p. In the first part (Sec. III), we use combinatorial methods, such as Young tableaux and Young subgroups, to construct a new basis for L(p) that respects this branching, and we express the basis elements explicitly in two distinct ways: first, as monomials of negative root vectors of g l (n) acting on certain g l (n) -highest weight vectors in L(p) and then as polynomials in the generators of o s p (1 | 2 n) acting on a o s p (1 | 2 n) -lowest weight vector in L(p). In the second part (Sec. IV), we use extremal projectors and the theory of Mickelsson–Zhelobenko algebras to give new explicit constructions of raising and lowering operators related to the branching o s p (1 | 2 n) ⊃ g l (n). We use the raising operators to give new expressions for the elements of the Gel'fand–Zetlin basis for L(p) as monomials of operators from U (o s p (1 | 2 n)) acting on a o s p (1 | 2 n) -lowest weight vector in L(p). We observe that the Gel'fand–Zetlin basis for L(p) is related to the basis constructed earlier in this paper by a triangular transition matrix. We end this paper (Sec. V) with a detailed example treating the case n = 3. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
14. Local 1/2-derivation on of n-dimensional naturally graded quasi-filiform Leibniz algebra of type I.
- Author
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Yusupov, Bakhtiyor, Vaisova, Nafosat, and Madrakhimov, Temur
- Subjects
- *
ALGEBRA , *LIE algebras - Abstract
For a given Lie algebra L, the main problem about local 1 2 -derivations is to prove that they automatically become an 1 2 -derivation or to give examples of local 1 2 -derivation of L, which are not 1 2 -derivation. In this paper, we investigate local 1 2 -derivations on quasi-filiform Leibniz algebras. It is proved that quasi-filiform Leibniz algebras of type I, as a rule, admit a local 1 2 -derivation which is not 1 2 -derivation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
15. 2-local automorphisms of arens algebras.
- Author
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Kalandarov, Turabay, Nasirov, Purxanatdin, Arziyeva, Rano, and Ongarbayev, Raxim
- Subjects
- *
VON Neumann algebras , *AUTOMORPHISMS , *NONCOMMUTATIVE algebras , *ALGEBRA , *BANACH spaces - Abstract
The focus of this paper is to examine 2-local automorphisms of the Arens algebra Lω (M,τ)) that is connected to a von Neumann algebra. Consider a von Neumann algebra M of type I accompanied by a trustworthy, regular, and semi-finite trace τ, we consider the noncommutative Arens algebra L ω (M , τ) = ∩ p ≥ 1 L p (M , τ) , where Lp (M,τ) is a Banach space defined Lp (M,τ)={x ∈ S(M,τ) :τ (| x |p)<∞} for p≥1. We will show that the surjective 2-local involutive automorphism Φ of the Arens algebra Lω (M,τ) identically acting on the center is an inner automorphism, i.e. there is a unitary element u of the Arens algebra Lω (M,τ) such that Φ(x)=uxu* for all x ∈ Lω (M,τ). It is required that the automorphism ϕx, y (x) for an arbitrary pair (x, y), satisfying the conditions ϕx, y (x)=Φ(x) and ϕx, y (y)=Φ(y), acts identically on the center of the Arens algebra. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
16. Special situation where the outer measure via order preserving valuation on a relative sub lattice obeys the outer measure generated by measure.
- Author
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Pramada, J., Rao, Y. V. Seshagiri, and Rao, T. Nageswara
- Subjects
VALUATION ,ALGEBRA ,MEASUREMENT - Abstract
This paper is motivated by GABOR SZASZ's introduction of outer measure based on valuation for lattices. We introduce order-preserving valuation on a relative sub lattice of the lattice, a countable cover of an element in a relative sub lattice, outer measure induced by a valuation of a relative sub lattice, Ɲ* measurability and to establish certain elementary properties of induced outer measure via order preserving valuation on a relative sub lattice. To prove outer measure via order preserving valuation on a relative sub lattice is also valid the outer measure generated by measure, we define the definition of outer measure on relative sub lattices of a lattice L induced by a measure Ɲ on Q of relative sub lattices of L, measure on algebra of relative sub lattices and outer measure of relative sub lattices, we prove L(ℬ) is a sigma-algebra where L(ℬ) is the class of Ɲ* measurable relative sub lattices and deduce a corollary that Ɲ*(S) = Ɲ(S), also we prove that outer measure to any subset E of a relative sub lattice SEQ
σ and outer measure to relative sub lattice BEQσδ are equal. Finally, by defining sigma-finite measure on Q and Ɲ* generated by Ɲ we prove a relative sub lattice E is measurable Ɲ* ⇔ E is the proper difference S ∼ B of a relative sub lattice A in Qσδ and a relative sub lattice B with Ɲ*(B) = 0. Further each relative sub lattice B with Ɲ*(B) = 0 is contained in a relative sub lattice C in Qσδ with Ɲ*(C) = 0. [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
17. Generalized Heisenberg–Virasoro algebra and matrix models from quantum algebra.
- Author
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Melong, Fridolin and Wulkenhaar, Raimar
- Subjects
MATRICES (Mathematics) ,ALGEBRA ,OPERATOR algebras - Abstract
In this paper, we construct the Heisenberg–Virasoro algebra in the framework of the R (p , q) -deformed quantum algebras. Moreover, the R (p , q) -Heisenberg–Witt n-algebras is also investigated. Furthermore, we generalize the notion of the elliptic Hermitian matrix models. We use the constraints to evaluate the R (p , q) -differential operators of the Virasoro algebra and generalize it to higher order differential operators. Particular cases corresponding to quantum algebras existing in the literature are deduced. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
18. Noncommutative geometry on central extension of U(u(2)).
- Author
-
Gurevich, Dimitry and Saponov, Pavel
- Subjects
GEOMETRY ,ALGEBRA ,SYMMETRY ,EQUATIONS - Abstract
In our previous publications, we have introduced analogs of partial derivatives on the reflection equation algebras, associated with Hecke symmetries. As a consequence, we get quantum partial derivatives on the enveloping algebras U(gl(N)). In the current paper, we consider the particular case N = 2 in detail and discuss the problem of a prolongation of these derivatives onto some central extension of the compact form U(u(2)) of the algebra U(gl(2)). Possible applications of this noncommutative geometry are discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
19. U(h)-free modules over the topological N = 2 super-BMS3 algebra.
- Author
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Lu, Hao, Sun, Jiancai, and Zhang, Honglian
- Subjects
ALGEBRA ,CLASSIFICATION - Abstract
In this paper, a class of non-weight modules over the topological N = 2 super-BMS
3 algebra g are completely constructed. Assume that h ̄ = C L 0 ⊕ C P 0 ⊕ C G 0 ⊕ C Q 0 is the Cartan subalgebra of g and h = C L 0 ⊕ C P 0 is a two-dimensional subalgebra of h ̄ . These modules over g are free of rank 2 as modules of the subalgebra h. In fact, these modules are reducible. Moreover, we give a complete classification of free U (h) -modules of rank 2 over g. [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
20. A new type restricted quantum group.
- Author
-
Xu, Yongjun and Chen, Jialei
- Subjects
QUANTUM groups ,HOPF algebras ,ALGEBRA - Abstract
In this paper, we define a new type restricted quantum group U ̄ q (s l 2 * ) and determine its Hopf Poincaré-Birkhoff-Witt-deformations U ̄ q (s l 2 * , κ) in which U ̄ q (s l 2 * , 0) = U ̄ q (s l 2 * ) and the classical restricted Drinfeld–Jimbo quantum group U ̄ q (s l 2 ) is included. We show that U ̄ q (s l 2 * ) is a basic Hopf algebra, then uniformly realize U ̄ q (s l 2 * ) and U ̄ q (s l 2 ) via some quotients of (deformed) preprojective algebras corresponding to the Gabriel quiver of U ̄ q (s l 2 * ). Moreover, we obtain a uniform tensor-categorical realization of U ̄ q (s l 2 * ) and U ̄ q (s l 2 ) , which is consistent with the above-mentioned Hopf-algebraic realization. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
21. Development of algorithms for the simulation environment to support the methodology of systems design based on automata models using HD-vector algebra.
- Author
-
Trokoz, Dmitriy, Martyshkin, Aleksey, Pashchenko, Dmitriy, Kalashnikov, Vitaliy, and Sinev, Michael
- Subjects
SYSTEMS design ,VECTOR algebra ,ALGEBRA ,ALGORITHMS ,INFORMATION storage & retrieval systems - Abstract
This paper presents the developed algorithms for a tool environment for the design of complex information systems based on automata models using the algebra of high-dimensional vectors. The paper raises the problem of the little knowledge of methods of coding complex systems in the format of automata based on the algebra of hyperdimensional vectors. Methods of formalized description of systems in the form of hyperdimensional vectors and description of algorithms for transformation of formalized description using the algebra of hyperdimensional vectors are introduced. The features, advantages and disadvantages of modeling automata models using hyperdimensional vectors are listed. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
22. Representations of the affine ageing algebra agê(1).
- Author
-
Li, Huaimin and Wang, Qing
- Subjects
- *
ALGEBRA , *AGE , *HECKE algebras , *SIMPLICITY , *AFFINE algebraic groups , *VERTEX operator algebras - Abstract
In this paper, we investigate the affine ageing algebra a g e ̂ (1) , which is a central extension of the loop algebra of the one-spatial ageing algebra a g e (1). Certain Verma-type modules including Verma modules and imaginary Verma modules of a g e ̂ (1) are studied. Particularly, the simplicity of these modules are characterized and their irreducible quotient modules are determined. We also study the restricted modules of a g e ̂ (1) which are also the modules of the affine vertex algebra arising from the one-spatial ageing algebra a g e (1). We present certain constructions of simple restricted a g e ̂ (1) -modules and an explicit such example of simple restricted module via the Whittaker module of a g e ̂ (1) is given. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
23. Irreducible modules over N = 2 superconformal algebras arising from algebraic D-modules.
- Author
-
Chen, Haibo, Dai, Xiansheng, Liu, Dong, and Pei, Yufeng
- Subjects
- *
ALGEBRA , *SUPERALGEBRAS , *ISOMORPHISM (Mathematics) - Abstract
In this paper, we introduce a family of functors denoted as F b , which act on algebraic D-modules and produce modules over N = 2 superconformal algebras. We demonstrate that these functors preserve irreducibility for all values of b, except for explicitly outlined cases. Moreover, we establish the necessary and sufficient conditions for determining the natural isomorphism between two such functors. Our constructed functors recover specific irreducible modules over N = 2 superconformal algebras, including intermediate series and U (h) -free modules. Additionally, we show that our constructed functors yield several new irreducible modules for N = 2 superconformal algebras. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. L∞-structures and cohomology theory of compatible O-operators and compatible dendriform algebras.
- Author
-
Das, Apurba, Guo, Shuangjian, and Qin, Yufei
- Subjects
- *
ASSOCIATIVE algebras , *ALGEBRA , *LIE algebras , *COHOMOLOGY theory - Abstract
The notion of O -operator is a generalization of the Rota–Baxter operator in the presence of a bimodule over an associative algebra. A compatible O -operator is a pair consisting of two O -operators satisfying a compatibility relation. A compatible O -operator algebra is an algebra together with a bimodule and a compatible O -operator. In this paper, we construct a graded Lie algebra and an L∞-algebra that respectively characterize compatible O -operators and compatible O -operator algebras as Maurer–Cartan elements. Using these characterizations, we define cohomology of these structures and as applications, we study formal deformations of compatible O -operators and compatible O -operator algebras. Finally, we consider a brief cohomological study of compatible dendriform algebras and find their relationship with the cohomology of compatible associative algebras and compatible O -operators. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
25. Drinfeld realization of the centrally extended psl(2|2) Yangian algebra with the manifest coproducts.
- Author
-
Matsumoto, Takuya
- Subjects
CONFORMAL field theory ,ALGEBRA ,HUBBARD model ,HOPF algebras ,NILPOTENT Lie groups - Abstract
The Lie superalgebra p s l (2 | 2) is recognized as a quite special algebra. In mathematics, it has the vanishing Killing form and allows for the three-dimensional central extension. In physics, it shows up as the symmetry of the one-dimensional Hubbard model and the asymptotic S-matrix of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. In this paper, we present the Drinfeld realization of the Yangian algebra associated with the centrally extended Lie superalgebra p s l (2 | 2). Furthermore, we show that it possesses Hopf algebra structures, particularly the coproducts. The idea to prove the existence of manifest coproducts is as follows. First, we shall introduce them to Levendorskii's realization, a system of a finite truncation of Drinfeld generators. Second, we show that Levendorskii's realization is isomorphic to the Drinfeld realization by induction. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
26. k-th singular locus moduli algebras of singularities and their derivation Lie algebras.
- Author
-
Ma, Guorui, Yau, Stephen S.-T., and Zuo, Huaiqing
- Subjects
LIE algebras ,ALGEBRA ,LOGICAL prediction - Abstract
In this paper, we introduce a series of new invariants for singularities. A new conjecture about the non-existence of negative weight derivations of the new k-th singular locus moduli algebras for weighted homogeneous isolated hypersurface singularities is proposed. We verify this conjecture in some cases. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
27. Twisted Rota–Baxter operators and Reynolds operators on Lie algebras and NS-Lie algebras.
- Author
-
Das, Apurba
- Subjects
LIE algebras ,OPERATOR algebras ,ALGEBRA ,R-matrices - Abstract
In this paper, we introduce twisted Rota–Baxter operators on Lie algebras as an operator analog of twisted r-matrices. We construct a suitable L
∞ -algebra whose Maurer–Cartan elements are given by twisted Rota–Baxter operators. This allows us to define the cohomology of a twisted Rota–Baxter operator. This cohomology can be seen as the Chevalley–Eilenberg cohomology of a certain Lie algebra with coefficients in a suitable representation. We study deformations of twisted Rota–Baxter operators from cohomological points of view. Some applications are given to Reynolds operators and twisted r-matrices. Next, we introduce a new algebraic structure, called NS-Lie algebras, that is related to twisted Rota–Baxter operators in the same way pre-Lie algebras are related to Rota–Baxter operators. We end this paper by considering twisted generalized complex structures on modules over Lie algebras. [ABSTRACT FROM AUTHOR]- Published
- 2021
- Full Text
- View/download PDF
28. Multiplicative polynomials and analytic functions on Fréchet algebras.
- Author
-
Labachuk, Oksana
- Subjects
ANALYTIC functions ,POLYNOMIALS ,TENSOR products ,ALGEBRA ,FUNCTION algebras - Abstract
In the paper multiplicative polynomials and analytic functions on Fréchet algebras are investigated. Some connections with homomorphisms on symmetric tensor products of the Fréchet algebras are obtained. A method of constructing of multiplicative G-analytic mapping on Fréchet algebras is proposed. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
29. Generating elements of the algebra of block-symmetric polynomials on the product of Banach spaces ℂs.
- Author
-
Kravtsiv, Viktoriia and Vitrykus, Diana
- Subjects
BANACH spaces ,ALGEBRA ,C*-algebras - Abstract
The paper contains a description of generating elements of algebras of block-symmetric polynomials on finite and infinite ℓ
p -sums of spaces ℂs , s ∈ ℕ. In the case of a finite sum and s > 1 there are no algebraic bases in these algebras and we propose explicit formulas for algebraic dependencies between generating elements. [ABSTRACT FROM AUTHOR]- Published
- 2022
- Full Text
- View/download PDF
30. A retrospective study on NTRU cryptosystem.
- Author
-
Mittal, Sonam and Ramkumar, K. R.
- Subjects
ENCRYPTION protocols ,DATA transmission systems ,CLOUD computing ,RETROSPECTIVE studies ,PUBLIC key cryptography ,CRYPTOGRAPHY ,RSA algorithm ,ALGEBRA - Abstract
Homomorphic Encryption, a magic wand in the field of cryptography that enables the user to perform secure computation over encrypted data, without decrypting the data. It allows cloud service providers to have access to encrypted data instead of original data, which also facilitates secure computation over encrypted data along with the secure transmission of it. NTRU, open-source public-key cryptography, based on lattices, is one of the standards of Homomorphic Encryption, can be used for secure outsourcing, the transmission of data, and performing computation on encrypted data. NTRU scheme is not vulnerable to quantum computer-based attacks, unlike existing traditional cryptographic techniques. In this paper, NTRU, the homomorphic encryption scheme is reviewed. The different variants of NTRU are also explainedthrough a detailed literature studybased on ring structure.The analysis also has been done that may help researchers to have a clear understanding of NTRU and its different variants and to distinguish them easily. The availability of different types of fields, rings based on different structures, different algebra, etc. for implementation of NTRU opens a new way for researchers to explore them to achieve a more efficient NTRU scheme for real-life applications. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
31. Noncommutative Yang model and its generalizations.
- Author
-
Meljanac, S. and Mignemi, S.
- Subjects
LORENTZ invariance ,GENERALIZATION ,SPACETIME ,PHASE space ,ALGEBRA ,BANACH algebras - Abstract
Long time ago, Yang [Phys. Rev. 72, 874 (1947)] proposed a model of noncommutative spacetime that generalized the Snyder model to a curved background. In this paper, we review his proposal and the generalizations that have been suggested during the years. In particular, we discuss the most general algebras that contain as subalgebras both de Sitter and Snyder algebras, preserving Lorentz invariance, and are generated by a two-parameter deformation of the canonical Heisenberg algebra. We also define their realizations on quantum phase space, giving explicit examples, both exact and in terms of a perturbative expansion in deformation parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
32. The fermionic integral on loop space and the Pfaffian line bundle.
- Author
-
Hanisch, Florian and Ludewig, Matthias
- Subjects
DIFFERENTIAL forms ,PATH integrals ,INTEGRALS ,ALGEBRA ,FINITE, The - Abstract
As the loop space of a Riemannian manifold is infinite-dimensional, it is a non-trivial problem to make sense of the "top degree component" of a differential form on it. In this paper, we show that a formula from finite dimensions generalizes to assign a sensible "top degree component" to certain composite forms, obtained by wedging with the exponential (in the exterior algebra) of the canonical presymplectic 2-form on the loop space. This construction is a crucial ingredient for the definition of the supersymmetric path integral on the loop space. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
33. Generalized quadratic commutator algebras of PBW-type.
- Author
-
Marquette, Ian, Yates, Luke, and D. Jarvis, Peter
- Subjects
COMMUTATION (Electricity) ,ALGEBRA ,GROBNER bases ,QUADRATIC equations ,COMMUTATORS (Operator theory) - Abstract
In recent years, various nonlinear algebraic structures have been obtained in the context of quantum systems as symmetry algebras, Painlevé transcendent models, and missing label problems. In this paper, we treat all these algebras as instances of the class of quadratic (and higher degree) commutator bracket algebras of Poincaré–Birkhoff–Witt type. We provide a general approach for simplifying the constraints arising from the diamond lemma and apply this in particular to give a comprehensive analysis of the quadratic case. We present new examples of quadratic algebras, which admit a cubic Casimir invariant. The connection with other approaches, such as Gröbner bases, is developed, and we suggest how our explicit and computational techniques can be relevant in other contexts. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
34. Differential graded vertex operator algebras and their Poisson algebras.
- Author
-
Caradot, Antoine, Jiang, Cuipo, and Lin, Zongzhu
- Subjects
- *
POISSON algebras , *DIFFERENTIAL algebra , *VERTEX operator algebras , *ALGEBRA - Abstract
In this paper, we define differential graded vertex operator algebras and the algebraic structures on the associated Zhu algebras and C2-algebras. We also introduce the corresponding notions of modules, and investigate the relations between the different module categories. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
35. The automorphism groups and derivation algebras of two-dimensional real algebras.
- Author
-
Bekbaev, Dilmurod
- Subjects
- *
AUTOMORPHISM groups , *GROUP algebras , *ALGEBRA , *AUTOMORPHISMS - Abstract
In this paper the classification theorem on two dimensional real algebras is used to describe their automorphism groups and derivation algebras. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
36. Holomorphic representation of Olshanetsky-Perelomov operators associated with the Weyl group of type Bn.
- Author
-
Nonkané, Ibrahim, Zongo, Frédéric D. Y., and Lawson, Latévi M.
- Subjects
- *
WEYL groups , *REPRESENTATIONS of groups (Algebra) , *HOLOMORPHIC functions , *DIFFERENTIAL operators , *VERTEX operator algebras , *ALGEBRA - Abstract
In this paper, we study the holomorphic representation of Olshanetsky-Perelomov operators associated with the weyl group W of type Bn. Thus, we view the algebra ℋ (ℂn) of holomorphic functions as a module the ring 풟 of invariant differential operators under the group W. Then we study the holomorphic representation of 풟. Using the representation theory of the Weyl group W, we construct the irreducible components of ℋ (ℂn), by explicity providing their generators. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
37. Holomorphic representation of Olshanetsky-Perelomov operators associated with the Weyl group of type Bn.
- Author
-
Nonkané, Ibrahim, Zongo, Frédéric D. Y., and Lawson, Latévi M.
- Subjects
WEYL groups ,REPRESENTATIONS of groups (Algebra) ,HOLOMORPHIC functions ,DIFFERENTIAL operators ,VERTEX operator algebras ,ALGEBRA - Abstract
In this paper, we study the holomorphic representation of Olshanetsky-Perelomov operators associated with the weyl group W of type B
n . Thus, we view the algebra ℋ (ℂn ) of holomorphic functions as a module the ring 풟 of invariant differential operators under the group W. Then we study the holomorphic representation of 풟. Using the representation theory of the Weyl group W, we construct the irreducible components of ℋ (ℂn ), by explicity providing their generators. [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
38. NSR singular vectors from Uglov polynomials.
- Author
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Bershtein, Mikhail and Vargulevich, Angelina
- Subjects
ALGEBRA ,LOGICAL prediction - Abstract
It was conjectured by Belavin et al. [J. High Energy Phys. 2013(3), 35] that bosonization of a singular vector (in the Neveu–Schwarz sector) of the N = 1 super analog of the Virasoro algebra can be identified with the Uglov symmetric function. In this paper, we prove this conjecture. We also extend this result to the Ramond sector of the N = 1 super-Virasoro algebra. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
39. U(h)-free modules over the super-Galilean conformal algebras.
- Author
-
Xie, Qiang, Sun, Jiancai, and Yang, Hengyun
- Subjects
ALGEBRA - Abstract
In this paper, we study non-weight modules over the super-Galilean conformal algebra. We construct and classify U (H) -free modules of rank 1 over the Ramond-type algebra and U (h) -free modules of rank 2 over the Neveu–Schwarz-type algebra, where H is a subalgebra of the Ramond-type algebra and h is the Cartan algebra of the Neveu–Schwarz-type algebra. We find that these modules are reducible and isomorphic. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
40. Possible ambient kinematics.
- Author
-
Morand, Kevin
- Subjects
- *
KINEMATICS , *LIE algebras , *SPACE-time symmetries , *IDEALS (Algebra) , *ALGEBRA - Abstract
In a seminal paper, Bacry and Lévy–Leblond classified kinematical algebras, a class of Lie algebras encoding the symmetries of spacetime. Homogeneous spacetimes (infinitesimally, Klein pairs) associated with these possible kinematics can be partitioned into four families—riemannian, lorentzian, galilean, and carrollian—based on the type of invariant metric structure they admit. In this work, we classify possible ambient kinematics—defined as extensions of kinematical algebras by a scalar ideal—as well as their associated Klein pairs. Kinematical Klein pairs arising as quotient space along the extra scalar ideal are said to admit a lift into the corresponding ambient Klein pair. While all non-galilean Klein pairs admit a unique—trivial and torsionfree—higher-dimensional lift, galilean Klein pairs are constructively shown to admit lifts into two distinct families of ambient Klein pairs. The first family includes the bargmann algebra as well as its curved/torsional avatars while the second family is novel and generically allows lifts into torsional ambient spaces. We further comment on the relation between these two families and the maximally symmetric family of leibnizian Klein pairs. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
41. Rota–Baxter family Ω-associative conformal algebras and their cohomology theory.
- Author
-
Zhang, Yuanyuan, Zhao, Jun, and Liu, Genqiang
- Subjects
- *
ALGEBRA , *YANG-Baxter equation , *COHOMOLOGY theory , *FAMILIES - Abstract
In this paper, we first propose the concept of Rota–Baxter family Ω-associative conformal algebras, then we study the cohomology theory of Rota–Baxter family Ω-associative conformal algebras of any weight and justify it by interpreting the lower degree cohomology groups as formal deformations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
42. Super modified KP hierarchy in Kac–van de Leur construction.
- Author
-
Chen, Huizhan, Cheng, Jipeng, and Wu, Zhiwei
- Subjects
LIE superalgebras ,DARBOUX transformations ,WAVE functions ,BILINEAR forms ,TENSOR products ,ALGEBRA - Abstract
In this paper, the modified KP hierarchy in the Kupershmidt–Kiso version is extended to the super case by Kac–van de Leur construction, that is, using highest weight representations of the even part in the tensor product of the infinite-dimensional Lie superalgebra gl
∞|∞ with Grassmann algebra G. First, the super modified KP (SmKP) hierarchy is constructed in terms of superfermionic bilinear equations. Then, the superbosonic form of the SmKP hierarchy is given by super boson–fermion correspondence. With the help of super Hirota bilinear operators, the corresponding super Hirota bilinear equations of the SmKP hierarchy are obtained. Next, the Darboux transformations of this new SmKP hierarchy are expressed in the form of free superfermions and various solutions are derived. Finally, the super bilinear equations in the form of super wave functions are also constructed from the superbosonic ones, which is hoped to be helpful to obtain the corresponding Lax structures. [ABSTRACT FROM AUTHOR]- Published
- 2022
- Full Text
- View/download PDF
43. A geometric algebraic study approach on the parallels between electromagnetism and fluid dynamics.
- Author
-
Pinheiro, Donna, Panakkal, Susan Mathew, Joseph, Bloomy, and Gomez, Noel J.
- Subjects
- *
FLUID dynamics , *ELECTROMAGNETISM , *MATHEMATICAL physics , *TOPOLOGICAL property , *ALGEBRA - Abstract
In this paper the correspondences between electromagnetic and fluid dynamic elements of many authors have been studied in detail, using the mathematical tool-geometric algebra. The physical as well as topological properties of the components are then analysed. Studying the different analogies indeed help to have a clear and compact visualisation of both fields and thus to understand the nature of their field mechanisms. The use of geometric algebra within mathematical physics, further envisages geometrical meaning as well as the physical interpretation of mathematical elements. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
44. New results of Q-bounded functional in symmetric Δ-Banach algebra.
- Author
-
Hussein, Boushra Y. and Wshayeh, Huda A. A.
- Subjects
- *
ALGEBRA - Abstract
This paper aims to present new results obtained from the study of the set of all self-adjoint elements and symmetric ideals of Æ. Also, include defining symmetric-representation linear functional on Æ. We define p and prove every p is state functional. We discuss a new functional is a q-bounded linear functional in Æ and discover some results depended on it. We define symmetric almost sublinear functional and depended on it since that every symmetric– representation of Æ is uniformly continuous. We introduce some results that discuss connected between every position linear functional in Æ is q-bounded linear functional if it is continuous functional. And we connect between every a positive linear functional on Æ is representable if satisfying q-bounded functional condition. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
45. Yang–Baxter algebra and MacMahon representation.
- Author
-
Wang, Na and Wu, Ke
- Subjects
REPRESENTATIONS of algebras ,SCHUR functions ,SPECIAL functions ,ALGEBRA ,POLYNOMIALS - Abstract
In this paper, we first prove that the affine Yangian of g l ̂ (1) is isomorphic to the algebra YB 0 g l ̂ (1) whose generators e
j , fj , ψj are defined using the Maulik–Okounkov R -matrix. Then, we provide the MacMahon representation of YB g l ̂ (1) which is generated by hj , ej , fj , ψj and find that the representation in the zero twist integrable system is isomorphic to the MacMahon representation. Finally, we discuss a special case in the zero twist integrable system, we obtain one kind of symmetric functions Y λ ( p ⃗) defined on two-dimensional Young diagrams, which are symmetric about the x-axis and y-axis, and the symmetric functions Y λ ( p ⃗) become Jack polynomials and Schur functions in special cases. [ABSTRACT FROM AUTHOR]- Published
- 2022
- Full Text
- View/download PDF
46. Quadratic and symplectic structures on 3-(Hom)–ρ-Lie algebras.
- Author
-
Bagheri, Zahra and Peyghan, Esmaeil
- Subjects
REPRESENTATIONS of algebras ,ALGEBRA ,LIE algebras - Abstract
In this paper, we generalize the notions of quadratic and symplectic structures to the case of 3-(Hom)–ρ-Lie algebras. We describe some properties of them by expressing the related lemmas and theorems. In addition, we introduce the concept of 3-pre-(Hom)–ρ-Lie algebras and define their representation. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
47. On fuzzy closed AlA – ideal of BRK – Algebra.
- Author
-
Abed, Alaa Saleh, Mohammed E, Showq, and Malik, Nidhal Kadhim
- Subjects
- *
ALGEBRA , *IDEALS (Algebra) - Abstract
In this paper, we characterize the ideas of an AlA – ideal of BRK – algebra, closed AlA – ideal of BRK – algebra, and a fuzzy closed AlA – ideal of BRK – algebra. Some kinds of stuff of these ideals and relate it with others are given. And we constructed and show some propositions of it. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
48. Domination of some zero divisor graph and it's complement.
- Author
-
Ghazi, Hayder F. and Omran, Ahmed A.
- Subjects
- *
COMPLETE graphs , *GRAPH theory , *BIPARTITE graphs , *ALGEBRA - Abstract
In this paper, the relationship between the algebra and graph theory are been studied especially the zero divisor graph in the ring ZN and constitute graph of these element Γ(Zn). The graph obtained by the above relation are isomorphic to some certain graphs as a complete and complete bipartite graph. The number of some vertices of Γ(Zn) are been introduced. Also, the domination of the zero divisor graph to some certain graphs are been determined. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
49. Generating elements of the algebra of block-symmetric polynomials on the product of Banach spaces ℂs.
- Author
-
Kravtsiv, Viktoriia and Vitrykus, Diana
- Subjects
- *
BANACH spaces , *ALGEBRA , *C*-algebras - Abstract
The paper contains a description of generating elements of algebras of block-symmetric polynomials on finite and infinite ℓp-sums of spaces ℂs, s ∈ ℕ. In the case of a finite sum and s > 1 there are no algebraic bases in these algebras and we propose explicit formulas for algebraic dependencies between generating elements. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
50. An innovative tripternion algebra for designing NTRU - like cryptosystem with high security.
- Author
-
Shahhadi, Sarah Hussain and Yassein, Hassan Rashed
- Subjects
- *
ALGEBRA , *INFORMATION technology security , *SECURITY management - Abstract
Due to the dependence on computers and the internet in many areas as a result of what it provides in terms of storing and transmitting information with high speed and accuracy, but there are many obstacles appeared when using a lot of computers, and the biggest of these obstacles and problems is the protection and securing of information that is stored in the computer and sent over the internet has become a necessity Urgency to the encryption system in order to maintain the security of the information and hide it so that even if it is reached, you ensure that they cannot understand it. NTRU is a good way to maintain information security characterized by its great resistance to attacks. In this paper we define a new multidimensional algebra called tripternion algebra and created a new algebraic structure to design analogue of NTRU public key cryptosystem which called NTRTRN with high security. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
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