{
  "id": "1008.2462",
  "version": "v1",
  "published": "2010-08-14T17:28:00.000Z",
  "updated": "2010-08-14T17:28:00.000Z",
  "title": "On cohomology of the Lie superalgebra D(2, 1 ; α)",
  "authors": [
    "Elena Poletaeva"
  ],
  "comment": "17 pages, to be published in Journal of Geometry and Physics 60(2010), 1771-1780",
  "doi": "10.1016/j.geomphys.2010.06.015",
  "categories": [
    "math.RT"
  ],
  "abstract": "We describe the infinitesimal deformations of the standard embedding of the Lie superalgebra $D(2, 1 ; \\alpha)$ into the Poisson superalgebra of pseudodifferential symbols on $S^{1|2}$. We show that for the standard embedding of $D(2, 1 ; \\alpha)$ into the Poisson superalgebra of differential operators on $S^{1|2}$, the infinitesimal deformations correspond to formal deformations. For the embedding of $D(2, 1 ; \\alpha)$ into the derived contact superconformal algebra ${K}'(4)$, the infinitesimal deformations are formal deformations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-14T17:28:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B56",
      "58H15"
    ],
    "keywords": [
      "lie superalgebra",
      "poisson superalgebra",
      "cohomology",
      "formal deformations",
      "derived contact superconformal algebra"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Geometry and Physics",
      "year": 2010,
      "month": "Nov",
      "volume": 60,
      "number": 11,
      "pages": 1771
    },
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JGP....60.1771P"
    }
  }
}