On Leibniz superalgebras which even part is 𝔰𝔩2

Abstract

This paper deals with Leibniz superalgebras [Formula: see text] whose even part is a simple Lie algebra [Formula: see text]. We describe all such Leibniz superalgebras when odd part is an irreducible Leibniz bi-module on [Formula: see text]. We show that there exist such Leibniz superalgebras with nontrivial odd part only in case of [Formula: see text]