{
  "id": "math/0202152",
  "version": "v1",
  "published": "2002-02-18T19:47:30.000Z",
  "updated": "2002-02-18T19:47:30.000Z",
  "title": "Defining relations for classical Lie superalgebras without Cartan matrices",
  "authors": [
    "Pavel Grozman",
    "Dimitry Leites",
    "Elena Poletaeva"
  ],
  "comment": "13p., Latex (this is an expanded version of the SQS'99 talk)",
  "journal": "In: E. Ivanov et. al. (eds.) Supersymmetries and Quantum Symmetries (SQS'99, 27--31 July, 1999), Dubna, JINR, 2000, 387--396; Homology, Homotopy and Applications, v 4(2), 2002, 259-275",
  "categories": [
    "math.RT"
  ],
  "abstract": "The analogs of Chevalley generators are offered for simple (and close to them) Z-graded complex Lie algebras and Lie superalgebras of polynomial growth without Cartan matrix. We show how to derive the defining relations between these generators and explicitly write them for a \"most natural\" (\"distinguished\" in terms of Penkov and Serganova) system of simple roots. The results are given mainly for Lie superalgebras whose component of degree zero is a Lie algebra (other cases being left to the reader). Observe presentations of exceptional Lie superalgebras and Lie superalgebras of hamiltonian vector fields. Now we can, at last, q-quantize the Lie Lie superalgebras of hamiltonian vector fields and Poisson superalgebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-02-18T19:47:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B65",
      "33C45",
      "33C80"
    ],
    "keywords": [
      "classical lie superalgebras",
      "defining relations",
      "cartan matrices",
      "hamiltonian vector fields",
      "z-graded complex lie algebras"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......2152G"
    }
  }
}