{
  "id": "0708.3191",
  "version": "v2",
  "published": "2007-08-23T15:30:32.000Z",
  "updated": "2007-11-20T14:58:32.000Z",
  "title": "Cohomology and Support Varieties for Lie Superalgebras II",
  "authors": [
    "Brian D. Boe",
    "Jonathan R. Kujawa",
    "Daniel K. Nakano"
  ],
  "comment": "28 pages, the proof of Proposition 4.5.1 was corrected, several other small errors were fixed",
  "doi": "10.1112/plms/pdn019",
  "categories": [
    "math.RT"
  ],
  "abstract": "In \\cite{BKN} the authors initiated a study of the representation theory of classical Lie superalgebras via a cohomological approach. Detecting subalgebras were constructed and a theory of support varieties was developed. The dimension of a detecting subalgebra coincides with the defect of the Lie superalgebra and the dimension of the support variety for a simple supermodule was conjectured to equal the atypicality of the supermodule. In this paper the authors compute the support varieties for Kac supermodules for Type I Lie superalgebras and the simple supermodules for $\\mathfrak{gl}(m|n)$. The latter result verifies our earlier conjecture for $\\mathfrak{gl}(m|n)$. In our investigation we also delineate several of the major differences between Type I versus Type II classical Lie superalgebras. Finally, the connection between atypicality, defect and superdimension is made more precise by using the theory of support varieties and representations of Clifford superalgebras.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-11-20T14:58:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B56",
      "17B10"
    ],
    "keywords": [
      "support variety",
      "classical lie superalgebras",
      "simple supermodule",
      "cohomology",
      "clifford superalgebras"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.3191B"
    }
  }
}