On Leibniz superalgebras which even part is sl2

This paper deals with Leibniz superalgebras L = L-0 circle plus 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 sl2(.) We show that there exist such Leibniz superalgebras with nontrivial odd part only in case of dim L-1 = 2.

Automated summary

This paper discusses Leibniz superalgebras L = L-0⊕L-1, with an even part being a simple Lie algebra sl(2), and describes all such Leibniz superalgebras when the odd part is an irreducible Leibniz bi-module on sl2(.). It is shown that Leibniz superalgebras with nontrivial odd parts exist only in the case of dim L-1 = 2.