{
  "id": "1004.1303",
  "version": "v4",
  "published": "2010-04-08T10:31:01.000Z",
  "updated": "2011-06-20T10:53:18.000Z",
  "title": "Endomorphism algebras of maximal rigid objects in cluster tubes",
  "authors": [
    "Dong Yang"
  ],
  "comment": "28 pages. The way of numbering subsections/propositions/theorems/lemmas/corollaries changed, several references added or updated, a few mistakes and typos corrected, some pictures added. To appear in Comm. Alg",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Given a maximal rigid object $T$ of the cluster tube, we determine the objects finitely presented by $T$. We then use the method of Keller and Reiten to show that the endomorphism algebra of $T$ is Gorenstein and of finite representation type, as first shown by Vatne. This algebra turns out to be the Jacobian algebra of a certain quiver with potential, when the characteristic of the base field is not 3. We study how this quiver with potential changes when $T$ is mutated. We also provide a derived equivalence classification for the endomorphism algebras of maximal rigid objects.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-06-20T10:53:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "16G10",
      "16E35"
    ],
    "keywords": [
      "maximal rigid object",
      "endomorphism algebra",
      "cluster tube",
      "finite representation type",
      "base field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.1303Y"
    }
  }
}