{
  "id": "0712.2970",
  "version": "v2",
  "published": "2007-12-18T14:23:12.000Z",
  "updated": "2009-02-10T16:11:40.000Z",
  "title": "Rigid objects in higher cluster categories",
  "authors": [
    "Anette Wrålsen"
  ],
  "comment": "2nd version 17 pages. More details have been added and some proofs have been improved. Some references have also been added",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study maximal $m$-rigid objects in the $m$-cluster category $\\mathcal C_H^m$ associated with a finite dimensional hereditary algebra $H$ with $n$ nonisomorphic simple modules. We show that all maximal $m$-rigid objects in these categories have exactly $n$ nonisomorphic indecomposable summands, and that any almost complete $m$-rigid object in $\\mathcal C_H^m$ has exactly $m+1$ nonisomorphic complements. We also show that the maximal $m$-rigid objects and the $m$-cluster tilting objects in these categories coincide, and that the class of finite dimensional algebras associated with maximal $m$-rigid objects is closed under certain factor algebras.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-02-10T16:11:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16G70"
    ],
    "keywords": [
      "cluster category",
      "rigid object",
      "higher cluster categories",
      "finite dimensional hereditary algebra",
      "nonisomorphic simple modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.2970W"
    }
  }
}