Classification of nilpotent Lie superalgebras of multiplier-rank $\leq 2$

TL;DR

This paper introduces the concept of multiplier-rank for Lie superalgebras and classifies all finite-dimensional nilpotent cases with multiplier-rank up to 2, including multipliers of Heisenberg superalgebras.

Contribution

It defines multiplier-rank for Lie superalgebras and provides a complete classification of nilpotent cases with multiplier-rank ≤ 2, expanding understanding of their structure.

Findings

Classified all nilpotent Lie superalgebras with multiplier-rank ≤ 2

Determined multipliers of Heisenberg superalgebras

Introduced the concept of super-multiplier-rank

Abstract

In this paper, we introduce the concept of (super-)multiplier-rank for Lie superalgeras and classify all the finite-dimensional nilpotent Lie superalgebras of multiplier-rank $\leq 2$ over an algebraically closed field of characteristic zero. In the process, we also determine the multipliers of Heisenberg superalgebras.