The classification of Leibniz superalgebras of nilindex n+m (m\neq 0)

Abstract

In this paper we investigate the description of the complex Leibniz superalgebras with nilindex n+m, where n and m ($m\ne 0$) are dimensions of even and odd parts, respectively. In fact, such superalgebras with characteristic sequence equal to $(n_1,...,n_k|m_1,...,m_s)$ (where $n_1+...+n_k=n,m_1+...+m_s=m$) for $n_1\ge n-1$ and $(n_1,...,n_k|m)$ were classified in works \cite{FilSup}--\cite{C-G-O-Kh1}. Here we prove that in the case of $(n_1,...,n_k|m_1,...,m_s)$, where $n_1\le n-2$ and $m_1\le m-1$ the Leibniz superalgebras have nilindex less than n+m. Thus, we complete the classification of Leibniz superalgebras with nilindex n+m.

18 pages, this manuscript complete the classification of Leibniz superalgebras of nilindex n+m

References in corpus (2)

• On the description of Leibniz superalgebras of nilindex n+m
• Classification of some nilpotent class of Leibniz superalgebras