On the Schur multiplier of nilpotent Lie superalgebra

Abstract

Let $L$ be an $(m|n)$-dimensional nilpotent Lie superalgebra where $m+n\ge 4$ and $n\ge 1$. This paper classifies such nilpotent Lie superalgebras $L$ with a derived subsuperalgebra of dimension $m+n-2$ such that $\gamma (L)=m+2n-2-\dim \mathcal{M}(L)$, where $\gamma (L)\in \{0,1,2\}$ and $\mathcal{M}(L)$ denotes the Schur multiplier of $L$. Furthermore, we show that all these superalgebras are capable.