On split regular BiHom-Leibniz superalgebras
Volume 161 / 2020
Colloquium Mathematicum 161 (2020), 295-309
MSC: Primary 17A30; Secondary 17B63.
DOI: 10.4064/cm7878-5-2019
Published online: 3 April 2020
Abstract
The goal of this paper is to study the structure of split regular BiHom-Leibniz superalgebras, which is a natural generalization of split regular Hom-Leibniz algebras and split regular BiHom-Lie superalgebras. By developing techniques of connections of roots for this kind of algebras, we show that a split regular BiHom-Leibniz superal\-gebra $\mathfrak {L}$ is of the form $\mathfrak {L}=U+\sum _{\alpha }I_\alpha $ with $U$ a subspace of a maximal abelian subalgebra $H$ and each $I_{\alpha }$ a well defined ideal of $\mathfrak {L}$ satisfying $[I_\alpha , I_\beta ]= 0$ if $\alpha \neq \beta $. In the case of $\mathfrak {L}$ of maximal length, the simplicity of $\mathfrak {L}$ is also characterized in terms of connections of roots.
