{
  "id": "0910.2077",
  "version": "v1",
  "published": "2009-10-12T03:55:07.000Z",
  "updated": "2009-10-12T03:55:07.000Z",
  "title": "Representations of Lie superalgebras in prime characteristic III",
  "authors": [
    "Lei Zhao"
  ],
  "comment": "17 pages, submitted for publication",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "For a restricted Lie superalgebra g over an algebraically closed field of characteristic p > 2, we generalize the deformation method of Premet and Skryabin to obtain results on the p-power and 2-power divisibility of dimensions of g-modules. In particular, we give a new proof of the Super Kac-Weisfeiler conjecture for basic classical Lie superalgebras. The new proof allows us to improve optimally the assumption on p. We also establish a semisimplicity criterion for the reduced enveloping superalgebras associated with semisimple p-characters for all basic classical Lie superalgebras using the technique of odd reflections.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-12T03:55:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B50"
    ],
    "keywords": [
      "prime characteristic",
      "basic classical lie superalgebras",
      "representations",
      "super kac-weisfeiler conjecture",
      "deformation method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.2077Z"
    }
  }
}