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arXiv · 1802.04468

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

Carlos Inostroza·Igor Kondrashuk·Nelson Merino·Felip Nadal
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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.

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Carlos Inostroza, Igor Kondrashuk, Nelson Merino, Felip Nadal. 2018-02-13. On a Java library to perform S-expansions of Lie algebras. https://doi.org/10.1088/1742-6596/1085/5/052010

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