On split regular Hom-Lie superalgebras (Preprint)

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Type: Preprint
National /International: International
Title: On split regular Hom-Lie superalgebras
Publication Date: 2024-01-23
Authors: - Helena Albuquerque
- Maria Elisabete Barreiro
- Antonio Jesus Calderón
- José María Sánchez Delgado
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+jIjwith \( U \) a linear subspace of a maximal abelian graded subalgebra H and any Ij a well described (split) ideal of \( \mathfrak L \) satisfying [Ij,Ik]=0 if jk. 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.

Institution: arXiv:2401.13710
Online version: https://arxiv.org/abs/2401.13710
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