{
  "id": "2501.15541",
  "version": "v1",
  "published": "2025-01-26T14:27:07.000Z",
  "updated": "2025-01-26T14:27:07.000Z",
  "title": "$\\mathbf{{\\mathbb Z}_2\\ \\times {\\mathbb Z}_2}$-graded Lie (super)algebras and generalized quantum statistics",
  "authors": [
    "N. I. Stoilova",
    "J. Van der Jeugt"
  ],
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "We present systems of parabosons and parafermions in the context of Lie algebras, Lie superalgebras, $\\mathbf{{\\mathbb Z}_2\\ \\times {\\mathbb Z}_2}$-graded Lie algebras and $\\mathbf{{\\mathbb Z}_2\\ \\times {\\mathbb Z}_2}$-graded Lie superalgebras. For certain relevant $\\mathbf{{\\mathbb Z}_2\\ \\times {\\mathbb Z}_2}$-graded Lie algebras and $\\mathbf{{\\mathbb Z}_2\\ \\times {\\mathbb Z}_2}$-graded Lie superalgebras, some structure theory in terms of roots and root vectors is developed. The short root vectors of these algebras are identified with parastatistics operators. For the $\\mathbf{{\\mathbb Z}_2\\ \\times {\\mathbb Z}_2}$-graded Lie algebra $so_q(2n+1)$, a system consisting of two ensembles of parafermions satisfying relative paraboson relations are introduced. For the $\\mathbf{{\\mathbb Z}_2\\ \\times {\\mathbb Z}_2}$-graded Lie superalgebra $osp(1,0|2n_1,2n_2)$, a system consisting of two ensembles of parabosons satisfying relative parafermion relations are introduced.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-26T14:27:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized quantum statistics",
      "graded lie algebra",
      "graded lie superalgebra",
      "satisfying relative paraboson relations",
      "satisfying relative parafermion relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}