{
  "id": "math/0609819",
  "version": "v2",
  "published": "2006-09-28T18:38:15.000Z",
  "updated": "2007-01-29T16:46:41.000Z",
  "title": "The small quantum group and the Springer resolution",
  "authors": [
    "Roman Bezrukavnikov",
    "Anna Lachowska"
  ],
  "comment": "MPIM preprint, to appear in Proceedings of Haifa Conference on Quantum Groups; the second version contains minor corrections",
  "categories": [
    "math.RT"
  ],
  "abstract": "In math.RT/0304173 the derived category of the principal block in modules over the Lusztig quantum algebra at a root of unity is related to the derived category of equivariant coherent sheaves on the Springer resolution. In the present paper we deduce a similar relation between the derived category of the principal block for the {\\em small (reduced) quantum algebra} and the derived category of (non-equivariant) coherent sheaves on the Springer resolution. As an application we get a geometric description of Hochschild cohomology (in particular, the center) of the regular block for the small quantum group, and use it to give an explicit description of a certain subalgebra in the center (obtained previously by another method and under more restrictive assumptions in math.QA/0107098. We also briefly explain the relation of our result to the geometric description math.RT/0407048 of the derived category of modules over the De Concini -- Kac quantum algebra.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-01-29T16:46:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "small quantum group",
      "springer resolution",
      "derived category",
      "principal block",
      "kac quantum algebra"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9819B"
    }
  }
}