{
  "id": "0901.1515",
  "version": "v5",
  "published": "2009-01-12T08:19:34.000Z",
  "updated": "2012-02-14T13:20:58.000Z",
  "title": "Mutation classes of \\tilde{A}_n-quivers and derived equivalence classification of cluster tilted algebras of type \\tilde{A}_n",
  "authors": [
    "Janine Bastian"
  ],
  "comment": "24 pages. v2: Correction of Definition 3.4. References added. Minor changes. v3: Revision of Definition 3.4 and Definition 3.9 (now 3.8). Proof of Lemma 3.7 (now 3.6) considerably simplified. Minor editorial changes. v4: Some examples omitted. Some proofs shortened. Minor editorial changes. v5: Final version. Minor editorial changes. arXiv admin note: text overlap with arXiv:math/0607348 by other authors",
  "doi": "10.2140/ant.2011.5.567",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We give an explicit description of the mutation classes of quivers of type \\tilde{A}_n. Furthermore, we provide a complete classification of cluster tilted algebras of type \\tilde{A}_n up to derived equivalence. We show that the bounded derived category of such an algebra depends on four combinatorial parameters of the corresponding quiver.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2012-02-14T13:20:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16E35",
      "18E30"
    ],
    "keywords": [
      "cluster tilted algebras",
      "derived equivalence classification",
      "mutation classes",
      "explicit description",
      "combinatorial parameters"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0901.1515B"
    }
  }
}