Results 1 to 10 of about 405 (136)
On the derivations of cyclic Leibniz algebras
Karpatsʹkì Matematičnì Publìkacìï, 2022 Let $L$ be an algebra over a field $F$. Then $L$ is called a left Leibniz algebra, if its multiplication operation $[-,-]$ additionally satisfies the so-called left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in L$. A linear
M.M. Semko, L.V. Skaskiv, O.A. Yarovaya
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On the derivations of Leibniz algebras of low dimension
Доповiдi Нацiональної академiї наук України, 2023 Let L be an algebra over a field F. Then L is called a left Leibniz algebra if its multiplication operations [×, ×] addition- ally satisfy the so-called left Leibniz identity: [[a,b],c] = [a,[b,c]] – [b,[a,c]] for all elements a, b, c Î L. In this paper,
L.A. Kurdachenko +2 more
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Description of the automorphism groups of some Leibniz algebras
Researches in Mathematics, 2023 Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[,]$. Then $L$ is called a left Leibniz algebra if it satisfies the left Leibniz identity: $[[a,b],c]=[a,[b,c]]-[b,[a,c]]$ for all elements $a,b,c\in L$.
L.A. Kurdachenko, O.O. Pypka, M.M. Semko
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On ideals and contraideals in Leibniz algebras
Доповiдi Нацiональної академiї наук України, 2023 A subalgebra S of a Leibniz algebra L is called a contraideal, if an ideal, generated by S coincides with L. We study the Leibniz algebras, whose subalgebras are either an ideal or a contraideal.
L.A. Kurdachenko +2 more
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On the algebra of derivations of some nilpotent Leibniz algebras
Researches in Mathematics, 2023 We describe the algebra of derivations of some nilpotent Leibniz algebra, having dimensionality 3.
L.A. Kurdachenko +2 more
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The Classical Hom–Leibniz Yang–Baxter Equation and Hom–Leibniz Bialgebras
Mathematics, 2022 In this paper, we first introduce the notion of Hom–Leibniz bialgebras, which is equivalent to matched pairs of Hom–Leibniz algebras and Manin triples of Hom–Leibniz algebras.
Shuangjian Guo +2 more
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Applying Group Theory Philosophy to Leibniz Algebras: Some New Developments [PDF]
Advances in Group Theory and Applications, 2020 This survey is an attempt of describing of main contours of a recently developing general theory of Leibniz Algebras. This theory based on the employing of methods and approaches which are proved to be exceedingly effective in infinite group theory.
Leonid A. Kurdachenko +2 more
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On the nilpotent Leibniz–Poisson algebras
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2012 In this article Leibniz and Leibniz–Poisson algebras in terms of correctness of different identities are investigated. We also examine varieties of these algebras. Let K be a base field of characteristics zero.
S. M. Ratseev, O. I. Cherevatenko
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On the influence of ideals and self-idealizing subalgebras on the structure of Leibniz algebras
Доповiдi Нацiональної академiї наук України, 2021 The subalgebra A of a Leibniz algebra L is self-idealizing in L, if A = IL (A) . In this paper we study the structure of Leibniz algebras, whose subalgebras are either ideals or self-idealizing.
L.A. Kurdachenko +2 more
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Maximal Solvable Leibniz Algebras with a Quasi-Filiform Nilradical
Mathematics, 2023 This article is part of a study on solvable Leibniz algebras with a given nilradical. In this paper, solvable Leibniz algebras, whose nilradical is naturally graded quasi-filiform algebra and the complemented space to the nilradical has maximal dimension,
Kobiljon Abdurasulov +2 more
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