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10 results on '"solvable algebras"'

5. Local and 2-local automorphisms of solvable Leibniz algebras with abelian and model nilradicals.

Author

Karimjanov, Iqboljon, Umrzaqov, Sardorbek, and Yusupov, Bakhtiyor

Subjects
ALGEBRA, AUTOMORPHISMS, LIE algebras
Abstract

In the paper, we describe the automorphisms on the solvable Leibniz algebras with the model or abelian nilradicals, whose complementary spaces are equal to two and one, respectively. We show that any local automorphism on a solvable Leibniz algebra with model nilradical of maximal codimension is an automorphism. We show that solvable Leibniz algebras with abelian nilradicals, which have 1-dimension complementary space, admit local automorphisms which are not automorphisms. Moreover, similar problems concerning 2-local automorphisms of such algebras are investigated. We give examples of solvable Leibniz algebras in which 2-local automorphisms are automorphisms and examples of such algebras which admit 2-local automorphisms which are not automorphisms. [ABSTRACT FROM AUTHOR]

Published
2024
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6. On evolution operators in characteristic 2.

Author

Varro, Richard

Subjects
NONASSOCIATIVE algebras, SCALAR field theory, ALGEBRA
Abstract

We are interested in the evolution operators defined on commutative and non-associative algebras when the characteristic of the scalar field is 2. We distinguish four types: nilpotent, quasi-constant, ultimately periodic, and plenary train operators. They are studied and classified for non-baric and for baric algebras. [ABSTRACT FROM AUTHOR]

Published
2021
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7. Local and 2-local derivations of solvable Leibniz algebras.

Author

Ayupov, Shavkat, Khudoyberdiyev, Abror, and Yusupov, Bakhtiyor

Subjects
*ALGEBRA
Abstract

We show that any local derivation on the solvable Leibniz algebras with model or abelian nilradicals, whose dimension of complementary space is maximal is a derivation. We show that solvable Leibniz algebras with abelian nilradicals, which have 1 dimension complementary space, admit local derivations which are not derivations. Moreover, similar problem concerning 2 -local derivations of such algebras is investigated and an example of solvable Leibniz algebra is given such that any 2 -local derivation on it is a derivation, but which admits local derivations which are not derivations. [ABSTRACT FROM AUTHOR]

Published
2020
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8. On the structure of Kac–Moody algebras

Author

Timothée Marquis and UCL - SST/IRMP - Institut de recherche en mathématique et physique

Subjects
Nipotent algebras, Pure mathematics, 010308 nuclear & particles physics, General Mathematics, 010102 general mathematics, Structure (category theory), Solvable algebras, Mathematics - Rings and Algebras, 01 natural sciences, Nilpotent, Bracket (mathematics), Rings and Algebras (math.RA), Homogeneous, Mathematics::Quantum Algebra, 0103 physical sciences, FOS: Mathematics, Cartan matrix, Kac-Moody algebras, 0101 mathematics, Algebra over a field, Element (category theory), Mathematics::Representation Theory, 17B67, 17B30, Mathematics
Abstract

Let $A$ be a symmetrisable generalised Cartan matrix, and let $\mathfrak g(A)$ be the corresponding Kac-Moody algebra. In this paper, we address the following fundamental question on the structure of $\mathfrak g(A)$: given two homogeneous elements $x,y \in \mathfrak g(A)$, when is their bracket $[x,y]$ a nonzero element? As an application of our results, we give a description of the solvable and nilpotent graded subalgebras of $\mathfrak g(A)$., 32 pages. Final version, to appear in Canadian Journal of Mathematics

Published
2020
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9. On the structure of Kac–Moody algebras

Author

UCL - SST/IRMP - Institut de recherche en mathématique et physique, Marquis, Timothée, UCL - SST/IRMP - Institut de recherche en mathématique et physique, and Marquis, Timothée

Abstract

Let $A$ be a symmetrisable generalised Cartan matrix, and let $\mathfrak g(A)$ be the corresponding Kac-Moody algebra. In this paper, we address the following fundamental question on the structure of $\mathfrak g(A)$: given two homogeneous elements $x,y\in\mathfrak g(A)$, when is their bracket $[x,y]$ a nonzero element? As an application of our results, we give a description of the solvable and nilpotent graded subalgebras of $\mathfrak g(A)$.

Published
2021

10. On evolution operators in characteristic 2

Author

Richard Varro, Institut Montpelliérain Alexander Grothendieck (IMAG), and Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Pure mathematics, evolution operators, evolution algebras, Algebra and Number Theory, solvable algebras, [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC], 010102 general mathematics, Bernstein algebras, 010103 numerical & computational mathematics, Secondary 17A30, 01 natural sciences, Nilpotent, quasiconstant algebras, Baric algebras, plenary train algebras, periodic Bernstein algebras, 0101 mathematics, 2010 MSC: Primary: 17D92, Secondary: 17A30, ultimately periodic operator 2010 MSC Primary 17D92, Scalar field, Commutative property, Mathematics, ultimately periodic operator
Abstract

International audience; We are interested in the evolution operators defined on commutative and non-associative algebras when the characteristic of the scalar field is 2. We distinguish four types: nilpotent, quasi-constant, ultimately periodic, and plenary train operators. They are studied and classified for non-baric and for baric algebras.

Published
2020
Full Text
View/download PDF

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