On Leibniz superalgebras which even part is sl_2

Abstract

This article deals with a Leibniz superalgebra L = L 0 ⊕ L 1 , whose even part is a simple Lie algebra sl 2 . We describe all such Leibniz superalgebras when odd part is an irreducible Leibniz bi-module on sl 2 . We show that there exist such Leibniz superalgebra with nontrivial odd part only in case of dimL 1 = 2.