On the description of Leibniz superalgebras of nilindex n+m

TL;DR

This paper classifies complex Leibniz superalgebras with a specific nilindex and characteristic sequence, extending previous classifications by analyzing cases where the sequence's first component is less than n-1.

Contribution

It proves that Leibniz superalgebras with certain characteristic sequences have nilindex less than n+m when the first sequence component is below n-1, completing the classification.

Findings

Superalgebras with n_1 < n-1 have nilindex less than n+m.

Complete classification of Leibniz superalgebras with characteristic sequence (n_1,...,n_k|m) and nilindex n+m.

Extended previous classifications to new cases where n_1 < n-1.

Abstract

In this work we investigate the complex Leibniz superalgebras with characteristic sequence $(n_1,...,n_k|m)$ and nilindex n+m, where $n=n_1+...+n_k,$ n and m (m is not equal to zero) are dimensions of even and odd parts, respectively. Such superalgebras with condition n_1 > n-2 were classified in \cite{FilSup}--\cite{C-G-O-Kh}. Here we prove that in the case $n_1 < n-1$ the Leibniz superalgebras have nilindex less than $n+m.$ Thus, we get the classification of Leibniz superalgebras with characteristic sequence $(n_1, ...,n_k|m)$ and nilindex n+m.