Solvable Leibniz superalgebras whose nilradical is a Lie superalgebra of maximal nilindex

Abstract

In this paper, we investigate solvable Leibniz superalgebras whose nilradical is a Lie superalgebra with maximal nilindex. It should be noted that Lie superalgebra with a maximal nilindex only exists in the variety of Lie2,m when m is odd. We give the classification of all solvable Leibniz superalgebras such that even part is a Lie algebra and nilradical is a Lie superalgebra with a maximal index of nilpotency.