Results 1 to 10 of about 71 (69)
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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The Leibniz algebras whose subalgebras are ideals
Open Mathematics, 2017 In this paper we obtain the description of the Leibniz algebras whose subalgebras are ideals.
Kurdachenko Leonid A. +2 more
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On the automorphism groups of some Leibniz algebras [PDF]
International Journal of Group Theory, 2023 We study the automorphism groups of finite-dimensional cyclic Leibniz algebras. In this connection, we consider the relationships between groups, modules over associative rings and Leibniz algebras.
Leonid Kurdachenko +2 more
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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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On Leibniz algebras with maximal cyclic subalgebras
Commentationes Mathematicae Universitatis Carolinae, 2023 We begin to study the structure of Leibniz algebras having maximal cyclic ...
Chupordia, Vasiliy A. +2 more
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On the structure of the algebra of derivations of cyclic Leibniz algebras
Algebra and Discrete Mathematics, 2021 We describe the algebra of derivation of finite-dimensional cyclic Leibniz algebra.
Kurdachenko, L.A. +2 more
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Methods of group theory in Leibniz algebras: some compelling results
Researches in Mathematics, 2021 The theory of Leibniz algebras has been developing quite intensively. Most of the results on the structural features of Leibniz algebras were obtained for finite-dimensional algebras and many of them over fields of characteristic zero.
I.Ya. Subbotin
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The description of the automorphism groups of finite-dimensional cyclic Leibniz algebras
Reports of the National Academy of Sciences of Ukraine, 2022 In the study of Leibniz algebras, the information about their automorphisms (as well as about endomorphisms, derivations, etc.) is very useful. We describe the automorphism groups of finite-dimensional cyclic Leibniz algebras. In particular, we consider the natural relationships between Leibniz algebras, groups and modules over associative rings.
L.A. Kurdachenko +2 more
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Leibniz algebras: a brief review of current results
Karpatsʹkì Matematičnì Publìkacìï, 2019 Let $L$ be an algebra over a field $F$ with the binary operations $+$ and $[\cdot,\cdot]$. 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 $a,b,c\in L$.
V.A. Chupordia +3 more
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, 2014 Leibniz algebras generated by one element, called cyclic, provide simple and illuminating examples of many basic concepts. It is the purpose of this paper to illustrate this fact.
Bugg, Kristin +4 more
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