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arXiv · 1903.12474

On split regular BiHom-Leibniz superalgebras

Shuangjian Guo·Shengxiang Wang
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Abstract

The goal of this paper is to study the structure of split regular BiHom-Leiniz superalgebras, which is a natural generalization of split regular Hom-Leiniz algebras and split regular BiHom-Lie superalgebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular BiHom-Leiniz superalgebras $\mathfrak{L}$ is of the form $\mathfrak{L}=U+\sum_{\a}I_\a$ with $U$ a subspace of a maximal abelian subalgebra $H$ and any $I_{\a}$, a well described ideal of $\mathfrak{L}$, satisfying $[I_\a, I_\b]= 0$ if $[\a]\neq [\b]$. In the case of $\mathfrak{L}$ being of maximal length, the simplicity of $\mathfrak{L}$ is also characterized in terms of connections of roots.

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Shuangjian Guo, Shengxiang Wang. 2019-03-28. On split regular BiHom-Leibniz superalgebras. https://arxiv.org/abs/1903.12474

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