{
  "id": "1802.04468",
  "version": "v1",
  "published": "2018-02-13T05:57:05.000Z",
  "updated": "2018-02-13T05:57:05.000Z",
  "title": "On a Java library to perform S-expansions of Lie algebras",
  "authors": [
    "Carlos Inostroza",
    "Igor Kondrashuk",
    "Nelson Merino",
    "Felip Nadal"
  ],
  "comment": "7 pages, 1 figure, Talk at ACAT 2017, Seattle, USA, to appear in Proceedings of ACAT 2017",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-13T05:57:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie algebra",
      "java library",
      "perform s-expansions",
      "extract smaller algebras",
      "finite abelian semigroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}