Certain functors of nilpotent Lie algebra with the derived subalgebra of dimension two

TL;DR

This paper investigates specific functors of nilpotent Lie algebras with a two-dimensional derived subalgebra, providing explicit computations of the Schur multiplier, exterior square, tensor square, and the corank.

Contribution

It offers new explicit calculations for these functors in a particular class of nilpotent Lie algebras, expanding understanding of their algebraic structure.

Findings

Computed the Schur multiplier for these Lie algebras

Determined the exterior and tensor squares explicitly

Established the corank of these Lie algebras

Abstract

By considering the nilpotent Lie algebra with the derived subalgebra of dimension $ 2$, we compute some functors include the Schur multiplier, the exterior square and the tensor square of these Lie algebras. We also give the corank of such Lie algebras.