{
  "id": "math-ph/0002031",
  "version": "v1",
  "published": "2000-02-10T02:57:38.000Z",
  "updated": "2000-02-10T02:57:38.000Z",
  "title": "Linear Odd Poisson Bracket on Grassmann Algebra",
  "authors": [
    "Vyacheslav A. Soroka"
  ],
  "comment": "8 pages, LATEX 2.09. The talk given at the International Seminar \"Supersymmetries and Quantum Symmetries\" (SQS'99, JINR, Dubna, Russia, 27-31 July, 1999). To be published in the Proceedings of this Seminar",
  "categories": [
    "math-ph",
    "hep-th",
    "math.GR",
    "math.MP"
  ],
  "abstract": "A linear odd Poisson bracket realized solely in terms of Grassmann variables is suggested. It is revealed that with the bracket, corresponding to a semi-simple Lie group, both a Grassmann-odd Casimir function and invariant (with respect to this group) nilpotent differential operators of the first, second and third orders are naturally related and enter into a finite-dimensional Lie superalgebra. A connection of the quantities, forming this Lie superalgebra, with the BRST charge, $\\Delta$-operator and ghost number operator is indicated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-02-10T02:57:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grassmann algebra",
      "linear odd poisson bracket",
      "grassmann-odd casimir function",
      "finite-dimensional lie superalgebra"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 513659,
      "adsabs": "2000math.ph...2031S"
    }
  }
}