On split regular BiHom-Leibniz superalgebras

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.

16pages. arXiv admin note: substantial text overlap with arXiv:1902.06260; text overlap with arXiv:1504.04236, arXiv:1508.02124 by other authors

References in corpus (3)

• Representations of Bihom-Lie algebras
• BiHom-Lie superalgebra structures
• Cohomology of Hom-Leibniz and $n$-ary Hom-Nambu-Lie superalgebras

Cited by in corpus (3)

• Construtions and bimodules of BiHom-alternative and BiHom-Jordan algebras
• Structures of BiHom-Poisson algebras
• Constructions and $T^{\ast }$-Extensions of 3-Bihom-Lie Superalgebras