On the classification of complex Leibniz superalgebras with characteristic sequence $(n-1, 1 | m_1, ..., m_k)$ and nilindex $n+m$

Abstract

In this work we investigate the complex Leibniz superalgebras with characteristic sequence $(n-1, 1 | m_1, ..., m_k)$ and with nilindex equal to $n+m.$ We prove that such superalgebras with the condition $m_2\neq0$ have nilindex less than $n+m$. Therefore the complete classification of Leibniz algebras with characteristic sequence $(n-1, 1 | m_1, ..., m_k)$ and with nilindex equal to $n+m$ is reduced to the classification of filiform Leibniz superalgebras of nilindex equal to $n+m,$ which was provided in \cite{AOKh} and \cite{GKh}.