On Leibniz superalgebras which even part is sl_2

Abstract

This article deals with a Leibniz superalgebras $L=L_0\oplus L_1,$ whose even part is a simple Lie algebra ${\mathfrak{sl}}_2$. We describe all such Leibniz superalgebras when odd part is an irreducible Leibniz bi-module on ${\mathfrak{sl}}_2$. We show that there exist such Leibniz superalgebras with nontrivial odd part only in case of $dim{L}_1=2.$

References in corpus (1)

• Finite-dimensional Leibniz algebra representations of ${\mathfrak{sl}}_2$