Results 21 to 30 of about 670,256 (260)

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, A.A. Pypka, N.N. Semko, V.S. Yashchuk   +3 more
doaj   +3 more sources

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
doaj   +2 more sources

ON LEVI’S THEOREM FOR LEIBNIZ ALGEBRAS [PDF]

Bulletin of the Australian Mathematical Society, 2011
AbstractA Lie algebra over a field of characteristic 0 splits over its soluble radical and all complements are conjugate. I show that the splitting theorem extends to Leibniz algebras but that the conjugacy theorem does not.
Donald W. Barnes
openalex   +4 more sources

Crossed Modules and Non-Abelian Extensions of Differential Leibniz Conformal Algebras

Axioms
In this paper, we introduce two-term differential Leib∞-conformal algebras and give characterizations of some particular classes of such two-term differential Leib∞-conformal algebras.
Hui Wu, Shuangjian Guo, Xiaohui Zhang
doaj   +2 more sources

Leibniz algebras with derivations [PDF]

Journal of Homotopy and Related Structures, 2021
Apurba Das
openalex   +3 more sources

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., Semko Nikolai N., Subbotin Igor Ya.   +2 more
doaj   +2 more sources

Nijenhuis operators on Leibniz algebras [PDF]

Journal of Geometry and Physics, 2023
In this paper, we study Nijenhuis operators on Leibniz algebras. We discuss the relationship of Nijenhuis operators with Rota-Baxter operators and modified Rota-Baxter operators on Leibniz algebras.
B. Mondal, R. Saha
semanticscholar   +1 more source

Subinvariance in Leibniz algebras [PDF]

Journal of Algebra, 2021
Leibniz algebras are certain generalizations of Lie algebras. Motivated by the concept of subinvariance in group theory, Schenkman studied properties of subinvariant subalgebras of a Lie algebra. In this paper we define subinvariant subalgebras of Leibniz algebras and study their properties.
Kailash C. Misra, Ernie Stitzinger, Xingjian Yu   +2 more
openaire   +3 more sources

On the representability of actions of Leibniz algebras and Poisson algebras [PDF]

Proceedings of the Edinburgh Mathematical Society, 2023
In a recent paper, motivated by the study of central extensions of associative algebras, George Janelidze introduces the notion of weakly action representable category.
A. S. Cigoli, Manuele Mancini, G. Metere
semanticscholar   +1 more source

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
doaj   +1 more source