{
  "id": "0705.1117",
  "version": "v1",
  "published": "2007-05-08T15:57:59.000Z",
  "updated": "2007-05-08T15:57:59.000Z",
  "title": "Quotients of cluster categories",
  "authors": [
    "Peter Jorgensen"
  ],
  "comment": "20 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Higher cluster categories were recently introduced as a generalization of cluster categories. This paper shows that in Dynkin types A and D, half of all higher cluster categories are actually just quotients of cluster categories. The other half can be obtained as quotients of 2-cluster categories, the \"lowest\" type of higher cluster categories. Hence, in Dynkin types A and D, all higher cluster phenomena are implicit in cluster categories and 2-cluster categories. In contrast, the same is not true in Dynkin type E.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-05-08T15:57:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "16G70",
      "18E30",
      "18E35"
    ],
    "keywords": [
      "higher cluster categories",
      "dynkin type",
      "higher cluster phenomena",
      "generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.1117J"
    }
  }
}