Geometrical aspects of the Lie Algebra S-Expansion Procedure

TL;DR

This paper explores how the S-Expansion procedure modifies the geometry of Lie groups, resulting in higher-dimensional Lie groups and non-simple Lie algebras, with methods to determine the semigroup involved.

Contribution

It provides a geometric analysis of the S-Expansion process and introduces a method to identify the semigroup that generates a new Lie algebra from an existing one.

Findings

S-Expansion alters the geometry of Lie groups, increasing their dimensionality.

The resulting Lie algebra from S-Expansion is non-simple.

A method is outlined to determine the semigroup for generating new Lie algebras.

Abstract

In this article it is shown that S-Expansion procedure affects the geometry of a Lie group, changing it an leading us to the geometry of another Lie group with higher dimensionality. Is outlined, via an example, a method for determining the semigroup, which would provide a Lie algebra from another. Finally, it is proved that the Lie algebra obtained from another Lie algebra via S-Expansion is a non-simple Lie algebra. I