{
  "id": "0809.0838",
  "version": "v1",
  "published": "2008-09-04T15:32:39.000Z",
  "updated": "2008-09-04T15:32:39.000Z",
  "title": "Cohomology of quantum groups: An analog of Kostant's Theorem",
  "authors": [
    "University of Georgia VIGRE Algebra Group",
    "Irfan Bagci",
    "Brian D. Boe",
    "Leonard Chastkofsky",
    "Benjamin Connell",
    "Benjamin Jones",
    "Wenjing Li",
    "Daniel K. Nakano",
    "Kenyon J. Platt",
    "Jae-Ho Shin",
    "Caroline B. Wright"
  ],
  "comment": "12 pages",
  "journal": "Proc. Amer. Math. Soc. 138 (2010), 85-99",
  "doi": "10.1090/S0002-9939-09-10039-4",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We prove the analog of Kostant's Theorem on Lie algebra cohomology in the context of quantum groups. We prove that Kostant's cohomology formula holds for quantum groups at a generic parameter $q$, recovering an earlier result of Malikov in the case where the underlying semisimple Lie algebra $\\mathfrak{g} = \\mathfrak{sl}(n)$. We also show that Kostant's formula holds when $q$ is specialized to an $\\ell$-th root of unity for odd $\\ell \\ge h-1$ (where $h$ is the Coxeter number of $\\mathfrak{g}$) when the highest weight of the coefficient module lies in the lowest alcove. This can be regarded as an extension of results of Friedlander-Parshall and Polo-Tilouine on the cohomology of Lie algebras of reductive algebraic groups in prime characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-09-04T15:32:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G42",
      "17B56"
    ],
    "keywords": [
      "quantum groups",
      "kostants theorem",
      "kostants cohomology formula holds",
      "coefficient module lies",
      "underlying semisimple lie algebra"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Proc. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.0838U"
    }
  }
}