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

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 $\le 2$ over an algebraically closed field of characteristic zero. In the process, we also determine the multipliers of Heisenberg superalgebras.

15 pages