On a Java library to perform S-expansions of Lie algebras
Carlos Inostroza, Igor Kondrashuk, Nelson Merino, Felip Nadal

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 with a finite abelian semigroup in such a way that a new S-expanded algebra 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 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.
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