On a Java library to perform S-expansions of Lie algebras

TL;DR

This paper introduces a Java library that automates the S-expansion method for Lie algebras, enabling systematic exploration and classification of algebraic relations through computational means.

Contribution

The paper presents a novel Java library that automates S-expansions of Lie algebras, facilitating analysis and classification of algebraic structures.

Findings

Library successfully automates S-expansion process

Enables classification of all possible S-expansions

Facilitates exploration of algebraic relations

Abstract

The S-expansion method is a generalization of the In\"{o}n\"{u}-Wigner (IW) contraction that allows to study new non-trivial relations between different Lie algebras. Basically, this method combines a Lie algebra $\mathcal{G}$ with a finite abelian semigroup $S$ in such a way that a new S-expanded algebra $\mathcal{G}_{S}$ can be defined. When the semigroup has a zero-element and/or a specific decomposition, which is said to be resonant with the subspace structure of the original algebra, then it is possible to extract smaller algebras from $\mathcal{G}_{S}$ which have interesting properties. Here we give a brief description of the S-expansion, its applications and the main motivations that lead us to elaborate a Java library, which automatizes this method and allows us to represent and to classify all possible S-expansions of a given Lie algebra.