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arXiv · 2401.12886

On split Leibniz superalgebras

Antonio J. Calderón·José M. Sánchez
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Abstract

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

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Antonio J. Calderón, José M. Sánchez. 2024-01-23. On split Leibniz superalgebras. https://doi.org/10.1016/j.laa.2013.01.017

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