{
  "id": "1604.07591",
  "version": "v1",
  "published": "2016-04-26T09:52:58.000Z",
  "updated": "2016-04-26T09:52:58.000Z",
  "title": "Hochschild cohomology of $q$-Schur algebras",
  "authors": [
    "Mayu Tsukamoto"
  ],
  "comment": "18 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We compute the Hochschild cohomology of any block of $q$-Schur algebras. We focus the even part of this Hochschild cohomology ring. To compute the Hochschild cohomology of $q$-Schur algebras, we prove the following two results: first, we construct two graded algebra surjections between the Hochschild cohomologies of quasi-hereditary algebras because all $q$-Schur algebras over a field are quasi-hereditary. Second, we give the graded algebra isomorphism of Hochschild cohomologies by using a certain derived equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-26T09:52:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G43",
      "16E40"
    ],
    "keywords": [
      "schur algebras",
      "quasi-hereditary algebras",
      "graded algebra surjections",
      "graded algebra isomorphism",
      "hochschild cohomology ring"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160407591T"
    }
  }
}