On Leibniz Superalgebras with Even Part Corresponding to $\mathfrak {sl}_{2}$

Abstract

In this paper we describe finite-dimensional complex Leibniz superalgebras whose even part is the simple Leibniz algebra corresponding to $\mathfrak {sl}_{2}$ , i.e. its quotient algebra with respect to the Leibniz kernel I is isomorphic to $\mathfrak {sl}_{2}$ . We classify these Leibniz superalgebras in several cases with arbitrary dimensions in which the odd part is essentially a Leibniz irreducible $(\mathfrak {sl}_{2} \dotplus I)$ -module or a finite direct sum of them.