{
  "id": "1601.00314",
  "version": "v1",
  "published": "2016-01-03T17:26:48.000Z",
  "updated": "2016-01-03T17:26:48.000Z",
  "title": "Periodicity of cluster tilting objects",
  "authors": [
    "Benedikte Grimeland"
  ],
  "comment": "32 pages. Comments welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let T be a locally finite triangulated category with an autoequivalence F such that the orbit category T/F is triangulated. We show that if X is an m-cluster tilting subcategory, then the image of X in T/F is an m-cluster tilting subcategory if and only if X is F-perodic. We show that for path-algebras of Dynking quivers \\delta one may study the periodic properties of n-cluster tilting objects in the n-cluster category Cn(k\\delta) to obtain information on periodicity of the preimage as n-cluster tilting subcategories of Db(k\\delta). Finally we classify the periodic properties of all 2-cluster tilting objects T of Dynkin quivers, in terms of symmetric properties of the quivers of the corresponding cluster tilted algebras EndC_2(T)^op. This gives a complete overview of all 2-cluster tilting objects of all triangulated orbit categories of Dynkin diagrams.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-03T17:26:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cluster tilting objects",
      "periodicity",
      "m-cluster tilting subcategory",
      "periodic properties",
      "orbit category t/f"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160100314G"
    }
  }
}