On split Leibniz superalgebras

Abstract

We study the structure of arbitrary split Leibniz superalgebras. We show that any of such superalgebras $\mathfrak{L}$ is of the form $\mathfrak{L}=\mathcal{U}+{\sum }_j{I}_j$ with $\mathcal{U}$ a subspace of an abelian (graded) subalgebra $H$ and any $I_j$ a well described (graded) ideal of $\mathfrak{L}$ satisfying $[I_j,I_k]=0$ if $j\ne k$. In the case of $\mathfrak{L}$ being of maximal length, the simplicity of $\mathfrak{L}$ is also characterized in terms of connections of roots.

arXiv admin note: text overlap with arXiv:2003.12607

References in corpus (5)

• n-Dimensional filiform Leibniz algebras of length (n-1) and their derivations
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Cited by in corpus (1)

• On the structure of split regular Hom-Lie Rinehart algebras