{
  "id": "math-ph/0409002",
  "version": "v1",
  "published": "2004-09-01T12:42:12.000Z",
  "updated": "2004-09-01T12:42:12.000Z",
  "title": "A classification of generalized quantum statistics associated with classical Lie algebras",
  "authors": [
    "N. I. Stoilova",
    "J. Van der Jeugt"
  ],
  "journal": "J.Math.Phys. 46 (2005) 033501",
  "doi": "10.1063/1.1827324",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP"
  ],
  "abstract": "Generalized quantum statistics such as para-Fermi statistics is characterized by certain triple relations which, in the case of para-Fermi statistics, are related to the orthogonal Lie algebra B_n=so(2n+1). In this paper, we give a quite general definition of ``a generalized quantum statistics associated to a classical Lie algebra G''. This definition is closely related to a certain Z-grading of G. The generalized quantum statistics is then determined by a set of root vectors (the creation and annihilation operators of the statistics) and the set of algebraic relations for these operators. Then we give a complete classification of all generalized quantum statistics associated to the classical Lie algebras A_n, B_n, C_n and D_n. In the classification, several new classes of generalized quantum statistics are described.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-01T12:42:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B20",
      "17B81",
      "81R05",
      "02.20.Sv",
      "05.30.Fk"
    ],
    "keywords": [
      "generalized quantum statistics",
      "classical lie algebra",
      "classification",
      "para-fermi statistics",
      "orthogonal lie algebra"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "J. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 658291
    }
  }
}