{
  "id": "math-ph/0603057",
  "version": "v1",
  "published": "2006-03-23T08:00:07.000Z",
  "updated": "2006-03-23T08:00:07.000Z",
  "title": "On the Cohomology of the Lie Superalgebra of Contact Vector Fields on $S^{1|2}$",
  "authors": [
    "Boujemaa Agrebaoui",
    "Nizar Ben Fraj",
    "Salem Omri"
  ],
  "comment": "Accepted for publication at the Journal of Nonlinear Mathematical Physics",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We investigate the first cohomology space associated with the embedding of the Lie superalgebra $\\cK(2)$ of contact vector fields on the (1,2)-dimensional supercircle $S^{1\\mid 2}$ in the Lie superalgebra $\\cS\\Psi \\cD \\cO(S^{1\\mid 2})$ of superpseudodifferential operators with smooth coefficients. Following Ovsienko and Roger, we show that this space is ten-dimensional with only even cocycles and we give explicit expressions of the basis cocycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-23T08:00:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "contact vector fields",
      "lie superalgebra",
      "basis cocycles",
      "first cohomology space",
      "explicit expressions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.2991/jnmp.2006.13.4.7",
      "journal": "Journal of Nonlinear Mathematical Physics",
      "year": 2006,
      "volume": 13,
      "number": 4,
      "pages": 523
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006JNMP...13..523A"
    }
  }
}