On the Schur multipliers of Lie superalgebras of maximal class

Abstract

We categorize all non-abelian nilpotent Lie superalgebras of dimension $(m|n)$, where $1\leq s(L)\leq 10$, and $s(L)$ is a non-negative integer defined by Nayak. Furthermore, we classify the structure of all Lie superalgebras of dimension at most five such that $\dim{L^2}=\dim\mathcal{M}(L)$.