Solvable Leibniz superalgebras whose nilradical has the characteristic sequence $(n-1, 1 \mid m)$ and nilindex $n+m$

TL;DR

This paper classifies solvable Leibniz superalgebras with a specific nilradical structure, providing conditions for their parameters and extending known classifications to include cases with maximal nilindex.

Contribution

It offers a complete classification of such superalgebras and determines parameter conditions for their solvable extensions, including cases with Lie superalgebra nilradicals.

Findings

Classification of solvable Leibniz superalgebras with nilindex n+m

Parameter conditions for solvable extensions

Extension to superalgebras with maximal nilindex

Abstract

Leibniz superalgebras with nilindex $n + m$ and characteristic sequence $(n-1, 1 \ | \ m)$ divided into four parametric classes that contain a set of non-isomorphic superalgebras. In this paper, we give a complete classification of solvable Leibniz superalgebras whose nilradical is a nilpotent Leibniz superalgebra with nilindex $n + m$ and characteristic sequence $(n-1, 1 \ | \ m)$. We obtain a condition for the value of parameters of the classes of such nilpotent superalgebras for which they have a solvable extension. Moreover, the classification of solvable Leibniz superalgebras whose nilradical is a Lie superalgebra with the maximal nilindex is given.