On $2$-Nilpotent Multiplier of Lie Superalgebras

TL;DR

This paper introduces the concept of the 2-nilpotent multiplier for finite-dimensional Lie superalgebras, characterizes its structure in specific cases, and explores bounds and capability properties of these algebraic structures.

Contribution

It defines the 2-nilpotent multiplier for Lie superalgebras and provides structural characterizations, bounds, and capability conditions for special classes.

Findings

Characterization of 2-nilpotent multiplier for certain nilpotent Lie superalgebras

Upper bounds on the dimension of 2-nilpotent multiplier

Analysis of 2-capability in specific Lie superalgebras

Abstract

In this article we define the $c$-nilpotent multiplier of a finite dimensional Lie suepralgebra. We characterize the structure of $2$-nilpotent multiplier of finite dimensional nilpotent Lie superalgebras whose derived subalgebras have dimension at most one. Then we give an upper bound on the dimension of $2$-nilpotent multiplier of any finite dimensional nilpotent Lie superalgebra. Moreover, we discuses the $2$-capability of special as well as odd Heisenberg Lie superalgebras and abelian Lie superalgebras.