2,659 results
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2. Classification of gyrogroups of orders at most 31.
- Author
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Ashrafi, Ali Reza, Nezhaad, Kurosh Mavaddat, and Salahshour, Mohammad Ali
- Subjects
AUTOMORPHISMS ,PRIME numbers ,INVERSE functions ,ASSOCIATIVITY (Propositional logic) ,BINARY operations - Abstract
A gyrogroup is defined as having a binary operation ⋆ containing an identity element such that each element has an inverse. Furthermore, for each pair (a, b) of elements of this structure, there exists an automorphism gyr[a, b] with the property that left associativity and the left loop property are satisfied. Since each gyrogroup is a left Bol loop, some results of Burn imply that all gyrogroups of orders p, 2p, and p², where p is a prime number, are groups. This paper aims to classify gyrogroups of orders 8, 12, 15, 18, 20, 21, and 28. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
3. On a paper of Beltrán and Shao about coprime action.
- Author
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Meng, H. and Ballester-Bolinches, A.
- Subjects
- *
FINITE groups , *MAXIMAL subgroups , *NILPOTENT Lie groups , *AUTOMORPHISMS - Abstract
Assume that A and G are finite groups of coprime orders such that A acts on G via automorphisms. Let p be a prime. The following coprime action version of a well-known theorem of Itô about the structure of a minimal non- p -nilpotent groups is proved: if every maximal A -invariant subgroup of G is p -nilpotent, then G is p -soluble. If, moreover, G is not p -nilpotent, then G must be soluble. Some earlier results about coprime action are consequences of this theorem. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
4. Infinitesimal Torelli for weighted complete intersections and certain Fano threefolds.
- Author
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Licht, Philipp
- Abstract
We generalize the classical approach of describing the infinitesimal Torelli map in terms of multiplication in a Jacobi ring to the case of quasi-smooth complete intersections in weighted projective space. As an application, we prove that the infinitesimal Torelli theorem does not hold for hyperelliptic Fano threefolds of Picard rank 1, index 1, degree 4, and study the action of the automorphism group on cohomology. The results of this paper are used to prove Lang-Vojta's conjecture for the moduli of such Fano threefolds in a follow-up paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
5. Automorphisms of symplectic totally isotropic subspace inclusion graph.
- Author
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He, Jianmei and Zhang, Gengsheng
- Subjects
SYMPLECTIC spaces ,AUTOMORPHISM groups ,MULTILINEAR algebra ,AUTOMORPHISMS - Abstract
Recently, symplectic totally isotropic subspace inclusion graph ℐ n () on a 2 ν -dimensional symplectic space was introduced in [J. He, S. Zhang and G. Zhang, Symplectic totally isotropic subspace inclusion graph, Linear Multilinear Algebra (2022), doi:10.1080/03081087.2022.2112016], which is a graph whose vertices are all totally isotropic subspaces of and two distinct vertices are adjacent if and only if one is contained in the other. In that paper, the authors studied the diameter, girth, clique number and chromatic number of ℐ n () and also studied some other properties of ℐ n (). In this paper, we determine the automorphism group of ℐ n (). [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
6. The biholomorphic invariance of essential normality on bounded symmetric domains.
- Author
-
Ding, Lijia
- Subjects
SYMMETRIC domains ,HILBERT modules ,KERNEL functions ,CALCULUS ,AUTOMORPHISMS - Abstract
This paper mainly concerns the biholomorphic invariance of p-essential normality of Hilbert modules on bounded symmetric domains. By establishing new integral formulas concerning rational function kernels for the Taylor functional calculus, we prove a biholomorphic invariance result related to the p-essential normality. Furthermore, for quotient analytic Hilbert submodules determined by analytic varieties, we develop an algebraic approach to proving that the p-essential normality is preserved invariant if the coordinate multipliers are replaced by arbitrary automorphism multipliers. Moreover, the Taylor spectrum of the compression tuple is calculated under a mild condition, which gives a solvability result of the corona problem for quotient submodules. As applications, we extend the recent results on the equivalence between \infty-essential normality and hyperrigidity. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
7. Action of automorphisms on irreducible characters of finite reductive groups of type 햠.
- Author
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Shirjian, Farrokh, Iranmanesh, Ali, and Shafiei, Farideh
- Subjects
FINITE groups ,STIMULUS generalization ,LINEAR algebraic groups ,AUTOMORPHISMS ,MATHEMATICS - Abstract
Let 퐺 be a finite reductive group such that the derived subgroup of the underlying algebraic group is a product of quasi-simple groups of type 햠. In this paper, we give an explicit description of the action of automorphisms of 퐺 on the set of its irreducible complex characters. This generalizes a recent result of M. Cabanes and B. Späth [Equivariant character correspondences and inductive McKay condition for type 햠, J. Reine Angew. Math.728 (2017), 153–194] and provides a useful tool for investigating the local sides of the local-global conjectures as one usually needs to deal with Levi subgroups. As an application we obtain a generalization of the stabilizer condition in the so-called inductive McKay condition [B. Späth, Inductive McKay condition in defining characteristic, Bull. Lond. Math. Soc.44 (2012), 3, 426–438; Theorem 2.12] for irreducible characters of 퐺. Moreover, a criterion is given to explicitly determine whether an irreducible character is a constituent of a given generalized Gelfand–Graev character of 퐺. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
8. On oriented m $m$‐semiregular representations of finite groups.
- Author
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Du, Jia‐Li, Feng, Yan‐Quan, and Bang, Sejeong
- Subjects
- *
AUTOMORPHISM groups , *FINITE groups , *AUTOMORPHISMS , *ORBITS (Astronomy) , *REPRESENTATIONS of groups (Algebra) - Abstract
A finite group G $G$ admits an
oriented regular representation if there exists a Cayley digraph of G $G$ such that it has no digons and its automorphism group is isomorphic to G $G$. Let m $m$ be a positive integer. In this paper, we extend the notion of oriented regular representations to oriented m $m$‐semiregular representations using m $m$‐Cayley digraphs. Given a finite group G $G$, an m $m$‐Cayley digraph of G $G$ is a digraph that has a group of automorphisms isomorphic to G $G$ acting semiregularly on the vertex set with m $m$ orbits. We say that a finite group G $G$ admits anoriented m $m$‐semiregular representation (Om $m$SR for short) if there exists an m $m$‐Cayley digraph Γ ${\rm{\Gamma }}$ of G $G$ such that it has no digons and G $G$ is isomorphic to its automorphism group. Moreover, if Γ ${\rm{\Gamma }}$ is regular, that is, each vertex has the same in‐ and out‐valency, we say Γ ${\rm{\Gamma }}$ is aregular oriented m $m$‐semiregular representation (regular Om $m$SR for short) of G $G$. In this paper, we classify finite groups admitting a regular Om $m$SR or an Om $m$SR for each positive integer m $m$. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
9. Topics in group schemes and surfaces in positive characteristic.
- Author
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Tziolas, Nikolaos
- Abstract
This paper is based on a series of talks that the author gave at the University of Edinburgh in March 2023 on surfaces in positive characteristic. In particular, infinitesimal group schemes and their actions on algebraic surfaces are discussed, the structure of the automorphism group scheme of a surface of general type and the failure of the Kodaira vanishing theorem. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
10. Characterization of (α, β) Jordan bi-derivations in prime rings.
- Author
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Ahmed, Wasim, Alali, Amal S., and Mozumder, Muzibur Rahman
- Subjects
AUTOMORPHISMS ,JORDAN algebras - Abstract
Let S be a prime ring with automorphisms α,β. A bi-additive map D is called an (α,β) Jordan bi-derivation if D(k2,s)=D(k,s)α(k)+β(k)D(k,s). In this paper, we find conditions under which a symmetric (α,β) Jordan bi-derivation becomes a symmetric (α,β) bi-derivation. We also characterize the symmetric (α,β) Jordan bi-derivations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
11. An AEC framework for fields with commuting automorphisms.
- Author
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Hyttinen, Tapani and Kangas, Kaisa
- Subjects
LINEAR orderings ,MODEL theory ,DIFFERENCE sets ,ENDOMORPHISMS ,AUTOMORPHISMS ,ENDOMORPHISM rings - Abstract
In this paper, we introduce an AEC framework for studying fields with commuting automorphisms. Fields with commuting automorphisms are closely related to difference fields. Some authors define a difference ring (or field) as a ring (or field) together with several commuting endomorphisms, while others only study one endomorphism. Z. Chatzidakis and E. Hrushovski have studied in depth the model theory of ACFA, the model companion of difference fields with one automorphism. Our fields with commuting automorphisms generalize this setting. We have several automorphisms and they are required to commute. Hrushovski has proved that in the case of fields with two or more commuting automorphisms, the existentially closed models do not necessarily form a first order model class. In the present paper, we introduce FCA-classes, an AEC framework for studying the existentially closed models of the theory of fields with commuting automorphisms. We prove that an FCA-class has AP and JEP and thus a monster model, that Galois types coincide with existential types in existentially closed models, that the class is homogeneous, and that there is a version of type amalgamation theorem that allows to combine three types under certain conditions. Finally, we use these results to show that our monster model is a simple homogeneous structure in the sense of S. Buechler and O. Lessman (this is a non-elementary analogue for the classification theoretic notion of a simple first order theory). [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
12. On the algebraic structure of quasi-group codes.
- Author
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Borello, Martino and Willems, Wolfgang
- Subjects
LINEAR codes ,PERMUTATION groups ,AUTOMORPHISMS ,AUTOMORPHISM groups ,PERMUTATIONS - Abstract
In this paper, an intrinsic description of some families of linear codes with symmetries is given, showing that they can be described more generally as quasi-group codes, that is, as linear codes allowing a group of permutation automorphisms which acts freely on the set of coordinates. An algebraic description, including the concatenated structure, of such codes is presented. This allows to construct quasi-group codes from codes over rings, and vice versa. The last part of the paper is dedicated to the investigation of self-duality of quasi-group codes. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
13. IDENTITIES WITH MULTIPLICATIVE GENERALIZED (α, α)-DERIVATIONS OF SEMIPRIME RINGS.
- Author
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SANDHU, GURNINDER SINGH, AYRAN, AYŞE, and AYDIN, NEŞET
- Subjects
COMMUTATIVE rings ,SEMIRINGS (Mathematics) ,AUTOMORPHISMS ,MORPHISMS (Mathematics) - Abstract
Let R be a semiprime ring and α be an automorphism of R. A mapping F : R → R (not necessarily additive) is called multiplicative generalized (α, α)- derivation if there exists a unique (α, α)-derivation d of R such that F(xy) = F(x)α(y) + α(x)d(y) for all x, y = R. In the present paper, we intend to study several algebraic identities involving multiplicative generalized (α, α)-derivations on appropriate subsets of semiprime rings and collect the information about the commutative structure of these rings. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
14. Generalized Shioda–Inose structures of order 3.
- Author
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Garbagnati, Alice and Prieto-Montañez, Yulieth
- Subjects
GEOMETRICAL constructions ,AUTOMORPHISMS ,ABELIAN functions - Abstract
A Shioda–Inose structure is a geometric construction which associates to an Abelian surface a projective K3 surface in such a way that their transcendental lattices are isometric. This geometric construction was described by Morrison by considering special symplectic involutions on the K3 surfaces. After Morrison several authors provided explicit examples. The aim of this paper is to generalize Morrison's results and some of the known examples to an analogous geometric construction involving not involutions, but order 3 automorphisms. Therefore, we define generalized Shioda–Inose structures of order 3, we identify the K3 surfaces and the Abelian surfaces which appear in these structures and we provide explicit examples. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
15. Flag-transitive 2-(v,k,λ) designs with λ prime and alternating socle.
- Author
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Zhang, Yongli, Chen, Jianfu, and Zhou, Shenglin
- Subjects
AUTOMORPHISM groups ,AUTOMORPHISMS - Abstract
This paper is a contribution to the classification of 2-designs admitting a flag-transitive automorphism group. Let be a 2- (v , k , λ) design with λ prime and G be a flag-transitive, point-primitive automorphism group of . We prove that if the socle of G is an alternating group, then has parameters (v , k , λ) = (1 5 , 7 , 3) , (6 , 3 , 2) , (1 0 , 6 , 5) or (1 0 , 4 , 2). [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
16. Hyperstability for a Generalized Class of Pexiderized Functional Equations on Monoids via Páles' Approach.
- Author
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Asharabi, Rashad M. and Almahalebi, Muaadh
- Subjects
ABELIAN groups ,MONOIDS ,FUNCTIONAL equations ,QUADRATIC equations ,AUTOMORPHISMS - Abstract
In this paper, we deduce some hyperstability results for a generalized class of homogeneous Pexiderized functional equations, expressed as ∑ ρ ∈ Γ f x ρ. y = ℓ f (x) + ℓ g (y) , x , y ∈ M , which is inspired by the concept of Ulam stability. Indeed, we prove that function f that approximately satisfies an equation can, under certain conditions, be considered an exact solution. Domain M is a monoid (semigroup with a neutral element), Γ is a finite subgroup of the automorphisms group of M, ℓ is the cardinality of Γ , and f , g : M → G such that (G , +) denotes an ℓ-cancellative commutative group. We also examine the hyperstability of the given equation in its inhomogeneous version ∑ ρ ∈ Γ f x ρ. y = ℓ f (x) + ℓ g (y) + ψ (x , y) , x , y ∈ M , where ψ : M × M → G . Additionally, we apply the main results to elucidate the hyperstability of various functional equations with involutions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
17. On α−Centralizer Mappings in Semiprime Rings.
- Author
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Sögütcü, E. Koç, Rehman, N., and Polat, S.
- Subjects
NILPOTENT Lie groups ,ADDITIVES ,AUTOMORPHISMS - Abstract
Let R be a 2−torsion free semiprime ring, α an automorphism and U a noncentral square-closed Lie ideal of R. An additive mapping T : R → R is called a left (resp. right) α−centralizer of R if T(xy) = T(x)α(y) (resp. T(xy) = α(x)T(y)) holds for all x, y ∈ R. In this paper, we proved the following result: i) If T (uvu) = α (u) T (v) α (u) for all u, v ∈ U, then T is a left α−centralizer, ii) If T(uvu) = T(u)α(vu) (resp. T(uvu) = α(uv)T(u)) for all u, v ∈ U, then T is a left (resp. right) α-centralizer on U. [ABSTRACT FROM AUTHOR]
- Published
- 2024
18. NON-INNER AUTOMORPHISMS OF ORDER p IN FINITE p-GROUPS OF COCLASS 4 AND 5.
- Author
-
PATALI, KOMMA
- Subjects
AUTOMORPHISMS ,LOGICAL prediction - Abstract
A long-standing conjecture asserts that every finite nonabelian p-group has a non-inner automorphism of order p. This paper proves the conjecture for finite p-groups of coclass 4 and 5 (p ≥ 5). We also prove the conjecture for an odd order nonabelian p-group G with cyclic center satisfying CG(Gpγ3(G)) ∩ Z3(G) ≤ Z(Φ(G)). [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
19. 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
20. Certain invariant multiplicative subset of a simple Artinian ring with involution. II.
- Author
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Chacron, M.
- Subjects
ARTIN rings ,AUTOMORPHISMS ,TRACE elements - Abstract
In the first part of the paper, we provide a fairly complete description of a simple ring R with involution f such that relative to f the traces of all elements of R form a commutative subset of R. This description is based on the characteristic of R. While the case of characteristic not 2 readily follows from current results in the literature, by contrast, the opposite case of characteristic 2 requires markedly more work. In the rest of the paper, the results carried out earlier are put to work to delineate the structure of a simple Artinian ring R with involution f, which is equipped with a given non central multiplicative subset M stabilized by f and preserved by all inner automorphisms of R, and such that the traces relative to f of all elements of M form a commutative subset of R. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
21. North-South type dynamics of relative atoroidal automorphisms of free groups on a relative space of currents.
- Author
-
Guerch, Yassine
- Subjects
NONABELIAN groups ,AUTOMORPHISM groups ,AUTOMORPHISMS ,TOPOLOGICAL spaces ,FREE groups ,HOMEOMORPHISMS ,COMPACT spaces (Topology) - Abstract
This paper, which is the second of a series of three papers, studies dynamical properties of elements of \operatorname {Out}(F_{\mathtt n}), the outer automorphism group of a nonabelian free group F_{\mathtt n}. We prove that, for every exponentially growing outer automorphism of F_{\mathtt n}, there exists a preferred compact topological space, the space of currents relative to a malnormal subgroup system, on which \phi acts by homeomorphism with a North-South dynamics behavior. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
22. Non-purely non-symplectic automorphisms of odd order on K3 surfaces.
- Author
-
Shingo TAKI
- Subjects
AUTOMORPHISMS - Abstract
In this paper we study non-symplectic automorphisms of odd order on K3 surfaces which are not purely. In particular we shall describe fixed loci of non-symplectic automorphisms of order 15 and 21. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
23. ON THE GRAPHS WITH DISTINGUISHING NUMBER EQUAL LIST DISTINGUISHING NUMBER.
- Author
-
ALIKHANI, S. and SOLTANI, S.
- Subjects
GRAPH theory ,NUMBER theory ,GEOMETRIC vertices ,AUTOMORPHISMS ,GRAPH labelings - Abstract
The distinguishing number D(G) of a graph G is the least integer d such that G has a vertex labeling with d labels that is preserved only by the trivial automorphism. A list assignment to G is an assignment L = {L(v)} v∈V (G) of lists of labels to the vertices of G. A distinguishing L-labeling of G is a distinguishing labeling of G where the label of each vertex v comes from L(v). The list distinguishing number of G, denoted by Dl(G), is the minimum k such that every list assignment to G in which |L(v)| = k for all v ∈ V (G) yields a distinguishing L-labeling of G. In this paper, we determine the list-distinguishing number for two families of graphs. We also characterize all graphs with the distinguishing number equal the list distinguishing number. Finally, we show that this characterization works for other list numbers of a graph. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
24. Isomorphism problems and groups of automorphisms for Ore extensions K[x][y; \delta] (zero characteristic).
- Author
-
Bavula, V. V.
- Subjects
ISOMORPHISM (Mathematics) ,GROUP algebras ,AUTOMORPHISM groups ,ORES ,AUTOMORPHISMS ,ALGEBRA ,POLYNOMIALS - Abstract
Let \Lambda (f) = K[x][y; f\frac {d}{dx} ] be an Ore extension of a polynomial algebra K[x] over a field K of characteristic zero where f\in K[x]. For a given polynomial f, the automorphism group of the algebra \Lambda (f) is explicitly described. The polynomial case \Lambda (0) = K[x,y] and the case of the Weyl algebra A_1= K[x][y; \frac {d}{dx} ] were done by Jung [J. Reine Angew. Math. 184 (1942), pp. 161–174] and van der Kulk [Nieuw Arch. Wisk. (3) 1 (1953), pp. 33–41], and Dixmier [Bul. Soc. Math. France 96 (1968), pp. 209–242], respectively. Alev and Dumas [Comm. Algebra 25 (1997), pp. 1655–1672] proved that the algebras \Lambda (f) and \Lambda (g) are isomorphic iff g(x) = \lambda f(\alpha x+\beta) for some \lambda, \alpha \in K\backslash \{ 0\} and \beta \in K. Benkart, Lopes and Ondrus [Trans. Amer. Math. Soc. 367 (2015), pp. 1993–2021] gave a complete description of the set of automorphism groups of algebras \Lambda (f). In this paper we complete the picture, i.e. given the polynomial f we have the explicit description of the automorphism group of \Lambda (f). The key concepts in finding the automorphism groups are the eigenform, the eigenroot and the eigengroup of a polynomial (introduced in the paper; they are of independent interest). [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
25. Condition-invariant and compact visual place description by convolutional autoencoder.
- Author
-
Ye, Hanjing, Chen, Weinan, Yu, Jingwen, He, Li, Guan, Yisheng, and Zhang, Hong
- Subjects
CONVOLUTIONAL neural networks ,VISUAL cryptography ,AUTOMORPHISMS - Abstract
Visual place recognition (VPR) in condition-varying environments is still an open problem. Popular solutions are convolutional neural network (CNN)-based image descriptors, which have been shown to outperform traditional image descriptors based on hand-crafted visual features. However, there are two drawbacks of current CNN-based descriptors: (a) their high dimension and (b) lack of generalization, leading to low efficiency and poor performance in real robotic applications. In this paper, we propose to use a convolutional autoencoder (CAE) to tackle this problem. We employ a high-level layer of a pre-trained CNN to generate features and train a CAE to map the features to a low-dimensional space to improve the condition invariance property of the descriptor and reduce its dimension at the same time. We verify our method in four challenging real-world datasets involving significant illumination changes, and our method is shown to be superior to the state-of-the-art. The code of our work is publicly available at https://github.com/MedlarTea/CAE-VPR. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
26. Some new properties of non-abelian tensor analogues of 2-auto Engel groups.
- Author
-
Sajedi, Mostafa and Darabi, Hamid
- Subjects
NILPOTENT groups ,TENSOR products ,AUTOMORPHISMS ,ABELIAN groups ,MATHEMATICAL proofs - Abstract
In this paper, we study the concept of 2
⊗ -auto Engel groups. Among other results, we prove that for any group G, if every element of G⊗Aut(G) is 2⊗ -Engel group, then ⟨ (g ⊗ α),(g ⊗ α) g′⊗α′ ⟩ is a nilpotent subgroup of class at most 2 in G ⊗ Aut(G), for all g, g′ ∈ G and α, α′ ∈ Aut(G). [ABSTRACT FROM AUTHOR]- Published
- 2023
27. Association schemes arising from table algebras
- Author
-
Xu, Bangteng
- Published
- 2023
- Full Text
- View/download PDF
28. Singular graphs with dicyclic or semi-dihedral group action.
- Author
-
Wu, Yongjiang, Yang, Jing, and Feng, Lihua
- Subjects
AUTOMORPHISMS ,EIGENVALUES ,CAYLEY graphs ,MULTIPLICITY (Mathematics) ,REGULAR graphs - Abstract
Let Γ be a finite simple graph with adjacency matrix A. Γ is said to be singular if and only if A has an eigenvalue 0. The nullity of Γ, denoted by null $ (\Gamma) $ (Γ) , is the multiplicity of the eigenvalue 0 in the spectrum of Γ. In this paper, we completely determine the singularity of graphs Γ for which the dicylic or semi-dihedral group acts transitively and faithfully on V as a group of automorphisms. Moreover, we give formulas to calculate the nullities for such graphs. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
29. LOCAL AUTOMORPHISMS OF n-DIMENSIONAL NATURALLY GRADED QUASI-FILIFORM LEIBNIZ ALGEBRA OF TYPE I.
- Author
-
ADASHEV, JOBIR and YUSUPOV, BAKHTIYOR
- Subjects
AUTOMORPHISMS ,LIE algebras ,MATHEMATICAL proofs ,SET theory ,ALGEBRAIC equations - Abstract
The notions of a local automorphism for Lie algebras are defined as similar to the associative case. Every automorphism of a Lie algebra L is a local automorphism. For a given Lie algebra L, the main problem concerning these notions is to prove that they automatically become an automorphism or to give examples of local automorphisms of L, which are not automorphisms. In this paper, we study local automorphisms on quasi-filiform Leibniz algebras. It is proved that quasi-filiform Leibniz algebras of type I, as a rule, admit local automorphisms which are not automorphisms. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
30. Genetic Algorithm-Based Method for Discovering Involutory MDS Matrices.
- Author
-
Bellfkih, El Mehdi, Nouh, Said, Chems Eddine Idrissi, Imrane, Louartiti, Khalid, and Mouline, Jamal
- Subjects
GENETIC algorithms ,ALGORITHMS ,CRYPTOGRAPHY ,AUTOMORPHISMS ,GROUP theory - Abstract
In this paper, we present an innovative approach for the discovery of involutory maximum distance separable (MDS) matrices over finite fields F 2 q , derived from MDS self-dual codes, by employing a technique based on genetic algorithms. The significance of involutory MDS matrices lies in their unique properties, making them valuable in various applications, particularly in coding theory and cryptography. We propose a genetic algorithm-based method that efficiently searches for involutory MDS matrices, ensuring their self-duality and maximization of distances between code words. By leveraging the genetic algorithm's ability to evolve solutions over generations, our approach automates the process of identifying optimal involutory MDS matrices. Through comprehensive experiments, we demonstrate the effectiveness of our method and also unveil essential insights into automorphism groups within MDS self-dual codes. These findings hold promise for practical applications and extend the horizons of knowledge in both coding theory and cryptographic systems. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
31. EXTENSIONS OF CHARACTERS IN TYPE D AND THE INDUCTIVE MCKAY CONDITION, I.
- Author
-
SPÄTH, BRITTA
- Subjects
- *
WEYL groups , *FINITE groups , *ORBITS (Astronomy) , *L-functions , *AUTOMORPHISMS , *MATHEMATICAL induction - Abstract
This is a contribution to the study of $\mathrm {Irr}(G)$ as an $\mathrm {Aut}(G)$ -set for G a finite quasisimple group. Focusing on the last open case of groups of Lie type $\mathrm {D}$ and $^2\mathrm {D}$ , a crucial property is the so-called $A'(\infty)$ condition expressing that diagonal automorphisms and graph-field automorphisms of G have transversal orbits in $\mathrm {Irr}(G)$. This is part of the stronger $A(\infty)$ condition introduced in the context of the reduction of the McKay conjecture to a question about quasisimple groups. Our main theorem is that a minimal counterexample to condition $A(\infty)$ for groups of type $\mathrm {D}$ would still satisfy $A'(\infty)$. This will be used in a second paper to fully establish $A(\infty)$ for any type and rank. The present paper uses Harish-Chandra induction as a parametrization tool. We give a new, more effective proof of the theorem of Geck and Lusztig ensuring that cuspidal characters of any standard Levi subgroup of $G=\mathrm {D}_{ l,\mathrm {sc}}(q)$ extend to their stabilizers in the normalizer of that Levi subgroup. This allows us to control the action of automorphisms on these extensions. From there, Harish-Chandra theory leads naturally to a detailed study of associated relative Weyl groups and other extendibility problems in that context. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
32. Regular maps with an alternating or symmetric group as automorphism group.
- Author
-
Conder, Marston D.E.
- Subjects
- *
AUTOMORPHISM groups , *MAPS , *AUTOMORPHISMS , *POLYHEDRA , *VALENCE (Chemistry) , *MORPHISMS (Mathematics) - Abstract
This paper provides a complete determination of which of the alternating groups A n and the symmetric groups S n occur as the automorphism group of some regular or chiral map on an orientable surface, and which of them occur as the automorphism group of a regular map on a non-orientable surface. The situation for some given types (m , k) is also considered, where k is the valency and m is the face-size, with special focus on types with m = 3 , and more particularly with (m , k) = (3 , 7) or (3 , 8) , or their duals. Some observations are made also about what happens for regular and orientably-regular maps with given valency, and for regular and chiral polyhedra. Much but certainly not all of what is presented follows from theorems in previous papers by the author and others, and this one brings them and some new observations together into a single reference. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
33. Automorphisms of Zappa-Szép product fixing a subgroup.
- Author
-
Kakkar, Vipul and Lal, Ratan
- Subjects
AUTOMORPHISM groups ,AUTOMORPHISMS ,CYCLIC groups ,FINITE groups - Abstract
In this paper, we have found the automorphism group of the Zappa-Szép product of two groups fixing a subgroup. We have computed these automorphisms for a subgroup of order p
2 of a group G which is the Zappa-Szép product of two cyclic groups in which one is of order p2 and other is of order m. [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
34. Construction of Asymptotically Good Locally Repairable Codes via Automorphism Groups of Function Fields.
- Author
-
Li, Xudong, Ma, Liming, and Xing, Chaoping
- Subjects
AUTOMORPHISM groups ,AUTOMORPHISMS ,JOB performance ,CIPHERS ,CONSTRUCTION ,CHAOTIC communication - Abstract
Locally repairable codes have been investigated extensively in recent years due to practical applications in distributed storage as well as theoretical interest. However, not much work on asymptotical behavior of locally repairable codes has been done until now. In particular, there is little result on constructive lower bound of asymptotical behavior of locally repairable codes. In this paper, we extend the construction given by Barg et al. via automorphism groups of function field towers. The main advantage of our construction is to allow more flexibility of locality. Furthermore, we show that the Gilbert–Varshamov type bound on locally repairable codes can be improved for all sufficiently large alphabet size $q$. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
35. On IA-isoclinism of groups.
- Author
-
Taheri, H.
- Subjects
FINITE groups ,PROBABILITY theory - Abstract
Let G be a group and IA (G) denote the group of all automorphisms of G which induces the identity mapping on the abelianization (i.e. G / G ′ ). Let IA z (G) be the subgroup of IA (G) such that fix the center element-wise. In this paper, we introduce the new concept of IA-isoclinism between two groups and prove similar results to the case of isoclinism including an application towards g -autocommuting probability of finite groups. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
36. Perfect state transfer on semi-Cayley graphs over abelian groups.
- Author
-
Arezoomand, Majid
- Subjects
ABELIAN groups ,CAYLEY graphs ,ORBITS (Astronomy) ,AUTOMORPHISMS - Abstract
In this paper, we consider the problem on the existence of perfect state transfer (PST for short) on semi-Cayley graphs over abelian groups (which are not necessarily regular), i.e. on the graphs having semiregular and abelian subgroups of automorphisms with two orbits of equal size. We stablish a characterization of semi-Cayley graphs over abelian groups having PST. As a result, we give a characterization of Cayley graphs over groups with an abelian subgroup of index 2 having PST, which improves the earlier results on Cayley graphs over abelian groups, dihedral groups and dicyclic group and determines Cayley graphs over generalized dihedral groups and generalized dicyclic groups having PST. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
37. Construction of Sequences With High Nonlinear Complexity From Function Fields.
- Author
-
Luo, Yuan, Xing, Chaoping, and You, Lin
- Subjects
AUTOMORPHISMS ,CYCLOTOMIC fields ,CRYPTOGRAPHY ,MATHEMATICAL sequences ,IRREDUCIBLE polynomials - Abstract
Complexity of sequences plays an important role in pseudorandom sequences and cryptography. In this paper, we present a construction of sequences with high nonlinear complexity from function fields. The main idea is to make use of function fields with many rational places as well as an automorphism of large order. We illustrate our construction through rational function fields and cyclotomic function fields in which there exist some automorphisms of large order. It turns out that we are able to: 1) slightly increase the length of the inversive sequence without losing nonlinear complexity and 2) obtain sequences with much larger nonlinear complexity than random sequences. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
38. Polynomial Automorphisms, Deformation Quantization and Some Applications on Noncommutative Algebras.
- Author
-
Zhang, Wenchao, Yavich, Roman, Belov-Kanel, Alexei, Razavinia, Farrokh, Elishev, Andrey, and Yu, Jietai
- Subjects
AUTOMORPHISMS ,POLYNOMIALS ,NONCOMMUTATIVE algebras ,QUANTUM groups ,HOMOMORPHISMS ,ALGEBRA ,TORUS ,GEOMETRIC quantization - Abstract
This paper surveys results concerning the quantization approach to the Jacobian Conjecture and related topics on noncommutative algebras. We start with a brief review of the paper and its motivations. The first section deals with the approximation by tame automorphisms and the Belov–Kontsevich Conjecture. The second section provides quantization proof of Bergman's centralizer theorem which has not been revisited for almost 50 years and formulates several related centralizer problems. In the third section, we investigate a free algebra analogue of a classical theorem of Białynicki-Birula's theorem and give a noncommutative version of this famous theorem. Additionally, we consider positive-root torus actions and obtain the linearity property analogous to the Białynicki-Birula theorem. In the last sections, we introduce Feigin's homomorphisms and we see how they help us in proving our main and fundamental theorems on screening operators and in the construction of our lattice W n -algebras associated with sl n , which is by far the simplest known approach concerning constructing such algebras until now. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
39. Algebraic Geometry. - New examples of tangentially degenerate curves.
- Author
-
Fukasawa, Satoru
- Subjects
ALGEBRAIC geometry ,GAUSS maps ,AUTOMORPHISMS - Abstract
This paper presents a method of constructing tangentially degenerate curves admitting a birational Gauss map, focusing on the non-classicality of automorphisms of the curves. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
40. Sixteen-dimensional compact translation planes with automorphism groups of dimension at least 35.
- Author
-
Löwe, Harald
- Subjects
AUTOMORPHISM groups ,ISOMORPHISM (Mathematics) ,MAXIMAL subgroups ,AUTOMORPHISMS - Abstract
The present paper investigates 16-dimensional compact translation planes with automorphism groups of dimension d between 35 and 37; planes with groups of higher dimensions have been classified by Hähl. We obtain a complete classification for d = 37 (up to isomorphisms). It turns out that these planes have Lenz type V and are already described in a recent paper of Hähl and Meyer [10]. Moreover, we give a partial classification for d = 35 and d = 36. The latter case will be completely finished in a forthcoming paper [16] of the author, while the case where d = 35 is completed except for groups whose maximal compact subgroups are 9-dimensional. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
41. The structure of filiform Lie algebra Q2m.
- Author
-
Sheng, Yuqiu and Yuan, Jixia
- Subjects
- *
COMMUTATIVE algebra , *LIE algebras , *LINEAR operators , *AUTOMORPHISMS , *MATRICES (Mathematics) - Abstract
This paper focuses on filiform Lie algebras Q2m in matrix version. We give the matrix forms of automorphisms (derivations) of Q2m. We prove that linear 2-local automorphisms (derivations) are automorphisms (derivations). Using the results of derivations of Q2m, we describe biderivations on Q2m. As application, we characterize linear commuting maps and the commutative Post-Lie algebra structures on Q2m. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
42. Endomorphisms of a variety of Ueno type and Kawaguchi–Silverman conjecture.
- Author
-
Oguiso, Keiji
- Subjects
- *
AUTOMORPHISM groups , *ENDOMORPHISMS , *LOGICAL prediction - Abstract
In this paper, we first show that the monoid of separable surjective self-morphisms of a variety of Ueno type coincides with the group of automorphisms. We also give an explicit description of the automorphism group. As applications, we confirm Kawaguchi–Silverman conjecture for automorphisms of a variety of Ueno type and some Calabi–Yau three-fold, defined over ℚ¯. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
43. Galois skew lines of smooth surfaces in P3.
- Author
-
Hayashi, Taro
- Subjects
- *
CYCLIC groups , *AUTOMORPHISMS - Abstract
AbstractIt is known that the degree of irrationality irr(X) of a smooth surface
X of degree d≥5 in P3 is at leastd – 2. In this paper, we study a Galois rational map f:X−−→P2 of degreed – 2, and we show that the Galois group off is a cyclic group, andf is defined by the family of lines intersecting two fixed skew lines. In addition, we give a necessary and sufficient condition thatX has skew lines which give a Galois rational map of degreed – 2 by using automorphisms ofX . [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
44. Adjacency preserving maps between tensor spaces.
- Author
-
Chooi, Wai Leong, Lau, Jinting, and Lim, Ming Huat
- Subjects
- *
ENDOMORPHISMS , *VECTOR spaces , *AUTOMORPHISMS - Abstract
Let r and s be positive integers such that r ⩾ 3. Let U 1 , ... , U r be vector spaces over a field F and V 1 , ... , V s be vector spaces over a field K such that dim U i , dim V j ⩾ 2 for all i , j. In this paper, we characterize maps ψ : ⨂ i = 1 r U i → ⨂ i = 1 s V i that preserve adjacency in both directions, which extends Hua's fundamental theorem of geometry of rectangular matrices. We also characterize related results concerning locally full maps preserving adjacency in both directions between tensor spaces, maps preserving adjacency in both directions between tensor spaces over a field all whose nonzero endomorphisms are automorphisms, and injective continuous adjacency preserving maps on finite dimensional tensor spaces over the real field. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
45. On the geometry and bounded cohomology of racks and quandles.
- Author
-
Kędra, Jarek
- Subjects
- *
AUTOMORPHISMS , *GEOMETRY , *COHOMOLOGY theory - Abstract
In this paper, we introduce and investigate a natural family of metrics on connected components of a rack. The metrics are closely related to certain bi-invariant metrics on the group of inner automorphisms of the rack. We also introduce a bounded cohomology of racks and quandles, relate them to the above metrics and prove a vanishing result for racks and quandles with amenable group of inner automorphisms. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
46. Automorphism Group of Green Algebra of Radford Hopf Algebra of Dimension Twelve.
- Author
-
Zhang, Xinru, Sun, Hua, and Chen, Huixiang
- Subjects
- *
AUTOMORPHISM groups , *GROUP algebras , *HOPF algebras , *AUTOMORPHISMS , *COMPLEX numbers , *GROUP rings - Abstract
Let H be the Radford Hopf algebra of dimension twelve over a field k . In this paper, we investigate the automorphism groups of the Green ring r(H) and the Green algebra ℂ(H) ≔ ℂ ⊗ℤr(H) over the complex number field ℂ. The ring automorphisms of r(H) and the algebra automorphisms of ℂ(H) are all described. It is shown that the ring automorphism group of r(H) is isomorphic to the Klein group K4, and the algebra automorphism group of ℂ(H) is isomorphic to the direct product ℂx × S4, where ℂx is the multiplicative group of all nonzero complex numbers and S4 is the symmetric group of degree 4. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
47. On automorphisms of tame polynomial automorphism Ind-Schemes in positive characteristic.
- Author
-
Kanel-Belov, Alexey, Elishev, Andrey, and Yu, Jie-Tai
- Subjects
- *
AUTOMORPHISMS , *AUTOMORPHISM groups , *POLYNOMIALS , *ALGEBRA - Abstract
AbstractIn this paper we study certain combinatorial attributes of Ind-schemes of polynomial automorphisms in positive characteristic. In particular, we prove that over an algebraically closed field
K of positive characteristic ≠2 every automorphism of the group of origin-preserving automorphisms of the polynomial algebra K[x1,…,xn] (n≥3), which fixes every diagonal matrix, preserves, up to composition with a linear inner automorphism, every tame automorphism. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
48. Automorphisms of simples Danielewski algebras.
- Author
-
El Kahoui, M’hammed and Hammi, Aziza
- Subjects
- *
ALGEBRA , *AUTOMORPHISMS , *CONCORD - Abstract
Let R be a commutative integral domain with unity that contains ℚ. In this paper we describe the R-automorphism group of R-algebras of the form R[x,y,z]/(c(x)z − q(x,y)), where c(x) ∈ R[x] is quasi-monic and q(x,y) ∈ R[x,y] is quasi-monic of degree at least two with respect to y. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
49. Local derivations and local automorphisms on the super Virasoro algebras.
- Author
-
Wu, Qingyan, Gao, Shoulan, Liu, Dong, and Ye, Chang
- Subjects
ALGEBRA ,AUTOMORPHISMS ,SUPERALGEBRAS - Abstract
This paper aims to study the local derivations, 2-local automorphisms and local automorphisms on the super-Virasoro algebras. The primary focus is to establish that every local derivation of the super-Virasoro algebras is indeed a derivation, and to demonstrate that every local or 2-local automorphism of the super-Virasoro algebras is an automorphism. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
50. Automorphisms of Chevalley groups over commutative rings.
- Author
-
Bunina, Elena
- Subjects
ABELIAN groups ,AUTOMORPHISM groups ,AUTOMORPHISMS ,COMMUTATIVE rings - Abstract
In this paper we prove that every automorphism of a Chevalley group (or its elementary subgroup) with root system of rank > 1 over a commutative ring (with 1/2 for the systems A 2 , F 4 , B l , C l ; with 1/2 and 1/3 for the system G 2 ) is standard, i.e., it is a composition of ring, inner, central and graph automorphisms. This result finalizes description of automorphisms of Chevalley groups. However, the restrictions on invertible elements can be a topic of further considerations. We provide also some model-theoretic applications of this description. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
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