Classification of finite dimensional nilpotent Lie superalgebras by their multiplier

Abstract

Let $L$ be a nilpotent Lie superalgebra of dimension $(m\mid n)$ and $s(L)=\frac{1}{2}[(m+n-1)(m+n-2)]+n+1-\dim \mathcal{M}(L)$, where $\mathcal{M}(L)$ denotes the Schur multiplier of $L$. Here $s(L)\ge 0$ and the structure of all non-abelian nilpotent Lie superalgebras with $s(L)=0$ is known((\cite{Nayak2019}). This paper is devoted to obtain all nilpotent Lie superalgebras when $s(L)\le 2$. Further, we apply those results to list all non-abelian nilpotent Lie superalgebras $L$ with $t(L)\le 4$.

arXiv comment19 pages