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Leibniz Algebras and Lie Algebras [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2013
This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking ...
Geoffrey Mason, Gaywalee Yamskulna
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Rota-Baxter Leibniz Algebras and Their Constructions

Advances in Mathematical Physics, 2018
In this paper, we introduce the concept of Rota-Baxter Leibniz algebras and explore two characterizations of Rota-Baxter Leibniz algebras. And we construct a number of Rota-Baxter Leibniz algebras from Leibniz algebras and associative algebras and ...
Liangyun Zhang, Linhan Li, Huihui Zheng
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On Inner Derivations of Leibniz Algebras

Mathematics
Leibniz algebras are generalizations of Lie algebras. Similar to Lie algebras, inner derivations play a crucial role in characterizing complete Leibniz algebras.
Sutida Patlertsin, Suchada Pongprasert, Thitarie Rungratgasame   +2 more
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Two-step nilpotent Leibniz algebras [PDF]

, 2022
Leibniz algebras were first introduced by J.-L. Loday as a non-antisymmetric version of Lie algebras, and many results of Lie algebras have been extended to Leibniz algebras. Earlier, such algebraic structures had been considered by A.
Manuel Mancini
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On Leibniz algebras with maximal cyclic subalgebras [PDF]

, 2022
summary:We begin to study the structure of Leibniz algebras having maximal cyclic ...
Subbotin, Igor Ya., Kurdachenko, Leonid A., Chupordia, Vasiliy A.   +2 more
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Biderivations of low-dimensional Leibniz algebras [PDF]

, 2023
In this paper we give a complete classification of the Leibniz algebras of biderivations of right Leibniz algebras of dimension up to three over a field $\mathbb{F}$, with $\operatorname{char}(\mathbb{F})\neq 2$.
Mancini, Manuel
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The c-nilpotent Schur Lie-multiplier of Leibniz algebras [PDF]

, 2023
We introduce the notion of c-nilpotent Schur Lie-multiplier of Leibniz algebras. We obtain exact sequences and formulas of the dimensions of the underlying vector spaces relating the c-nilpotent Schur Lie-multiplier of a Leibniz algebra q and its ...
Biyogmam, G.R., Casas Mirás, José Manuel   +1 more
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Pre-derivations and description of non-strongly nilpotent filiform Leibniz algebras [PDF]

, 2021
summary:In this paper we give the description of some non-strongly nilpotent Leibniz algebras. We pay our attention to the subclass of nilpotent Leibniz algebras, which is called filiform. Note that the set of filiform Leibniz algebras of fixed dimension
Khudoyberdiyev, A.Kh., Abdurasulov, K.K., Ladra, M., Sattarov, A.M., Khudoyberdiyev, A. Kh.   +4 more
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Notes on Leibniz n-algebras [PDF]

, 2023
We analyze behaviors of generalized forgetful and Daletskii-Takhtajan’s functors on perfect objects and crossed modules of Leibniz n-algebras. Then we give applications to homology and universal central extensions of Leibniz n-algebrasAgencia Estatal de ...
Ladra González, Manuel, Khmaladze, Emzar, Casas Mirás, José Manuel   +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, Jobir Adashev, Ivan Kaygorodov   +2 more
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