On split regular Hom-Lie superalgebras

Abstract

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 $\mathfrak{L}$ is of the form $\mathfrak{L}=U+{\sum }_j{I}_j$ with $U$ a linear subspace of a maximal abelian graded subalgebra $H$ and any $I_j$ a well described (split) ideal of $\mathfrak{L}$ satisfying $[I_j,I_k]=0$ if $j\ne k$. Under certain conditions, the simplicity of $\mathfrak{L}$ is characterized and it is shown that $\mathfrak{L}$ is the direct sum of the family of its simple ideals.

References in corpus (1)

• Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras

Cited by in corpus (5)

• On split regular BiHom-Leibniz superalgebras
• On the structure of split regular Hom-Lie Rinehart algebras
• On split regular Hom-Leibniz-Rinehart algebras
• Split 3-Lie-Rinehart color algebras
• On split regular BiHom-Poisson superalgebras