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

Abstract

The S-expansion method is a generalization of the Inönü-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.

7 pages, 1 figure, Talk at ACAT 2017, Seattle, USA, to appear in Proceedings of ACAT 2017