Related papers: On split regular BiHom-Leibniz superalgebras
The paper introduces the class of split regular BiHom-Poisson superalgebras, which is a natural generalization of split regular Hom-Poisson algebras and split regular BiHom-Lie superalgebras. By developing techniques of connections of roots…
We introduce the class of split regular Hom-Leibniz algebras as the natural generalization of split Leibniz algebras and split regular Hom-Lie algebras. By developing techniques of connections of roots for this kind of algebras, we show…
We study the structure of arbitrary split Leibniz superalgebras. We show that any of such superalgebras ${\frak L}$ is of the form ${\frak L} = {\mathcal U} + \sum_jI_j$ with ${\mathcal U}$ a subspace of an abelian (graded) subalgebra $H$…
We introduce the class of split regular Hom-Lie superalgebras as the natural extension of the one of split Hom-Lie algebras and Lie superalgebras, and study its structure by showing that an arbitrary split regular Hom-Lie superalgebra…
In this paper, we introduce the notion of the Hom-Leibniz-Rinehart algebra as an algebraic analogue of Hom-Leibniz algebroid, and prove that such an arbitrary split regular Hom-Leibniz-Rinehart algebra $L$ is of the form $L=U+\sum_\gamma…
We introduce the class of split regular Hom-Lie color algebras as the natural generalization of split Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Lie…
The aim of this paper is to study the structures of split regular Hom-Lie Rinehart algebras. Let $(L,A)$ be a split regular Hom-Lie Rinehart algebra. We first show that $L$ is of the form $L=U+\sum_{[\gamma]\in\Gamma/\thicksim}I_{[\gamma]}$…
We introduce and describe the class of split regular $Hom$-Leibniz color $3$-algebras as the natural extension of the class of split Lie algebras, split Leibniz algebras, split Lie $3$-algebras, split Lie triple systems, split Leibniz…
Consider a Leibniz superalgebra $\mathfrak L$ additionally graded by an arbitrary set $I$ (set grading). We show that $\mathfrak L$ decomposes as the sum of well-described graded ideals plus (maybe) a suitable linear subspace. In the case…
We study the structures of arbitrary split $\delta$ Jordan-Lie algebras with symmetric root systems. We show that any of such algebras $L$ is of the form $L = U + \sum\limits_{[j] \in \Lambda/\sim}I_{[j]}$ with $U$ a subspace of $H$ and any…
The aim of this paper is to introduce the notion of BiHom-Lie superalgebras. This class of algebras is a generalization of both BiHom-Lie algebras and Hom-Lie superalgebras. In this article, we first present two ways to construct BiHom-Lie…
BiHom-superdialgebras are clear generalization of Hom-superdialgebras. The purpose of this note is to describe and to survey structures of BiHom-superdialgebras. Then we derive derivations of BiHomsuperdialgebras.
From the Levi's Theorem it is known that every finite dimensional Lie algebra over a field of characteristic zero is decomposed into semidirect sum of solvable radical and semisimple subalgebra. Moreover, semisimple part is the direct sum…
In order to study the structure of arbitrary split Leibniz triple systems, we introduce the class of split Leibniz triple systems as the natural extension of the class of split Lie triple systems and split Leibniz algebras. By developing…
The aim of this paper is to introduce $n$-ary BiHom-algebras, generalizing BiHom-algebras. We introduce an alternative concept of BiHom-Lie algebra called BiHom-Lie-Leibniz algebra and study various type of $n$-ary BiHom-Lie algebras and…
The first aim of this paper is to introduce and study symmetric (Bi)Hom-Leibniz algebras, which are left and right Leibniz algebras. We discuss $\alpha^k\beta^l$-generalized derivations, $\alpha^k\beta^l$ -quasi-derivations and…
We present matrices as graded BiHom-algebras and consider various characteristics of their decompositions. Specifically, we introduce a notion of connection in the support of the grading and use it to construct a family of canonical graded…
In this paper we identify the structure of complex finite-dimensional Leibniz algebras with associated Lie algebras $sl_2^1\oplus sl_2^2\oplus \dots \oplus sl_2^s\oplus R,$ where $R$ is a solvable radical. The classifications of such…
We study the structure of graded Lie superalgebras with arbitrary dimension and over an arbitrary field ${\mathbb K}$. We show that any of such algebras ${\mathfrak L}$ with a symmetric $G$-support is of the form ${\mathfrak L} = U +…
The structure of Lie algebras, Lie superalgebras and Leibniz algebras graded by finite root systems has been studied by several researchers since 1992. In this paper, we study the structure of Leibniz superalgebras graded by finite root…