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On split Leibniz superalgebras (2401.12886v1)
Published 23 Jan 2024 in math.RA
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.