Detecting capable pairs of some nilpotent Lie superalgebras

TL;DR

This paper introduces the concept of capable pairs of Lie superalgebras, classifies them for specific types, and analyzes their Schur multipliers, advancing the understanding of their algebraic structure.

Contribution

It defines capable pairs of Lie superalgebras, classifies capable pairs for abelian and Heisenberg types, and explores their Schur multipliers, providing new structural insights.

Findings

Classified all capable pairs of abelian and Heisenberg Lie superalgebras.

Analyzed pairs with derived subalgebra of dimension one and non-abelian ideal.

Determined the structure of the Schur multiplier for pairs of Heisenberg Lie superalgebras.

Abstract

In this article, we define the capable pairs of Lie superalgebras. We classify all capable pairs of abelian and Heisenberg Lie superalgebras. After that we discuss on pairs of Lie superalgebras with derived subalgebra of dimension one and a non-abelian ideal. Finally, we determine the structure of the Schur multiplier of pairs of Heisenberg Lie superalgebras.