English

On split Leibniz superalgebras

Rings and Algebras 2024-01-24 v1

Abstract

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

Keywords

Cite

@article{arxiv.2401.12886,
  title  = {On split Leibniz superalgebras},
  author = {Antonio J. Calderón and José M. Sánchez},
  journal= {arXiv preprint arXiv:2401.12886},
  year   = {2024}
}

Comments

arXiv admin note: text overlap with arXiv:2003.12607

R2 v1 2026-06-28T14:24:55.072Z