{
  "id": "2204.11395",
  "version": "v1",
  "published": "2022-04-25T01:58:56.000Z",
  "updated": "2022-04-25T01:58:56.000Z",
  "title": "Decomposition of enveloping algebras of simple Lie algebras and their related polynomial algebras",
  "authors": [
    "Rutwig Campoamor-Stursberg",
    "Ian Marquette"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The decomposition problem of the enveloping algebra of a simple Lie algebra is reconsidered combining both the analytical and the algebraic approach, showing its relation with the internal labelling problem with respect to a nilpotent subalgebra. A lower bound for the number of generators of the commutant as well as the maximal Abelian subalgebra are obtained. The decomposition problem for the exceptional Lie algebra $G_2$ is completely solved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-25T01:58:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple lie algebra",
      "related polynomial algebras",
      "enveloping algebra",
      "decomposition problem",
      "exceptional lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}