Application of superalgebra homology groups to distinguish Engel-like structures

TL;DR

This paper demonstrates how homology groups of Lie superalgebras can be used to classify 4-dimensional Engel-like Lie algebras, providing a novel algebraic approach to their distinction.

Contribution

It introduces a new application of superalgebra homology groups for classifying Engel-like Lie algebras, expanding algebraic classification methods.

Findings

Homology groups effectively distinguish different Engel-like structures.

The approach applies to three types of Lie superalgebras on manifolds.

Provides a new tool for algebraic classification of low-dimensional Lie algebras.

Abstract

There are three kinds of Lie superalgebras for each differentiable manifold. In this note, we shall show an application of the homology groups of those superalgebras in order to classify 4 dimensional Engel-like Lie algebras.