A characterization of finite dimensional nilpotent Lie superalgebras

Abstract

Let $L$ be a nilpotent Lie superalgebras of dimension $(m\mid n)$ for some non-negative integers $m$ and $n$ and put $s(L) = \frac{1}{2}[(m + n - 1)(m + n -2)]+ n+ 1 - \dim \mathcal{M}(L)$, where $\mathcal{M}(L)$ denotes the Schur multiplier of $L$. Recently, the author has shown that $s(L) \geq 0$ and the structure of all nilpotent Lie superalgebras has been determined when $s(L) = 0$ \cite{Nayak2018}. The aim of this paper is to classify all nilpotent Lie superalgebras $L$ for which $s(L) = 1$ and $2$.Comment: 19 page