Results 1 to 10 of about 39,842 (129)

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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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 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, M.M. Semko, V.S. Yashchuk   +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, Shengxiang Wang, Xiaohui Zhang   +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, Nikolai N. Semko, Igor Ya. Subbotin   +2 more
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Cohomology of nonabelian embedding tensors on Hom-Lie algebras

AIMS Mathematics, 2023
In this paper, we generalize known results of nonabelian embedding tensor to the Hom setting. We introduce the concept of Hom-Leibniz-Lie algebra, which is the basic algebraic structure of nonabelian embedded tensors on Hom-Lie algebras and can also be ...
Wen Teng , Jiulin Jin, Yu Zhang
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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, Jobir Adashev, Ivan Kaygorodov   +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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From Groups to Leibniz Algebras: Common Approaches, Parallel Results [PDF]

Advances in Group Theory and Applications, 2018
In this article, we study (locally) nilpotent and hyper-central Leibniz algebras. We obtained results similar to those in group theory. For instance, we proved a result analogous to the Hirsch-Plotkin Theorem for locally nilpotent groups.
L.A. Kurdachenko, I.Ya. Subbotin, N.N. Semko   +2 more
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Automorphisms of the universal enveloping algebra of a finite-dimensional Zinbiel algebra with zero multiplication

Қарағанды университетінің хабаршысы. Математика сериясы, 2023
In recent years there has been a great interest in the study of Zinbiel (dual Leibniz) algebras. Let A be Zinbiel algebra over an arbitrary field K and let e1,e2,...,em,... be a linear basis of A. In 2010 A.
D.M. Zhangazinova, A.S. Naurazbekova
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