On the Schur multipliers of Lie superalgebras of maximal class

TL;DR

This paper classifies specific nilpotent Lie superalgebras based on their Schur multipliers and structure, providing a comprehensive understanding of their properties for dimensions up to five and a parameter s(L) up to 10.

Contribution

It offers a complete classification of non-abelian nilpotent Lie superalgebras with bounded s(L) and characterizes those with equal derived and Schur multiplier dimensions.

Findings

Classified all non-abelian nilpotent Lie superalgebras with 1 ≤ s(L) ≤ 10.

Determined the structure of Lie superalgebras of dimension ≤ 5 with equal derived and Schur multiplier dimensions.

Provided explicit descriptions of these superalgebras' structures.

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 $\dim{L^2}=\dim\mathcal{M}(L)$.