English

On Leibniz superalgebras which even part is sl_2

Rings and Algebras 2019-05-03 v1

Abstract

This article deals with a Leibniz superalgebras L=L0L1,L=L_0\oplus L_1, whose even part is a simple Lie algebra sl2\mathfrak{sl}_2. We describe all such Leibniz superalgebras when odd part is an irreducible Leibniz bi-module on sl2\mathfrak{sl}_2 . We show that there exist such Leibniz superalgebras with nontrivial odd part only in case of dimL1=2.dim L_1=2.

Keywords

Cite

@article{arxiv.1905.00845,
  title  = {On Leibniz superalgebras which even part is sl_2},
  author = {Kh. A. Khalkulova and A. Kh. Khudoyberdiyev},
  journal= {arXiv preprint arXiv:1905.00845},
  year   = {2019}
}