{
  "id": "1307.1322",
  "version": "v2",
  "published": "2013-07-04T13:33:39.000Z",
  "updated": "2013-07-22T20:18:09.000Z",
  "title": "Homological algebra for osp(1/2n)",
  "authors": [
    "Kevin Coulembier"
  ],
  "journal": "Avances in Lie Superalgebras, Springer Indam Series, Gorelik and Papi (2014), 19-34",
  "categories": [
    "math.RT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We discuss several topics of homological algebra for the Lie superalgebra osp(1|2n). First we focus on Bott-Kostant cohomology, which yields classical results although the cohomology is not given by the kernel of the Kostant quabla operator. Based on this cohomology we can derive strong Bernstein-Gelfand-Gelfand resolutions for finite dimensional osp(1|2n)-modules. Then we state the Bott-Borel-Weil theorem which follows immediately from the Bott-Kostant cohomology by using the Peter-Weyl theorem for osp(1|2n). Finally we calculate the projective dimension of irreducible and Verma modules in the category O.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-22T20:18:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B55",
      "18G10",
      "17B10"
    ],
    "keywords": [
      "homological algebra",
      "bott-kostant cohomology",
      "derive strong bernstein-gelfand-gelfand resolutions",
      "kostant quabla operator",
      "lie superalgebra"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.1322C"
    }
  }
}