{
  "id": "math/0612451",
  "version": "v3",
  "published": "2006-12-15T17:16:34.000Z",
  "updated": "2010-02-19T13:43:48.000Z",
  "title": "Cluster categories, selfinjective algebras, and stable Calabi-Yau dimensions: types D and E",
  "authors": [
    "Thorsten Holm",
    "Peter Jorgensen"
  ],
  "comment": "This preprint has been withdrawn",
  "categories": [
    "math.RT"
  ],
  "abstract": "The preprints arXiv:math/0610728 and arXiv:math/0612451 are withdrawn due to a problem with Theorem 2.2 in arXiv:math/0610728. The theorem claims that for certain triangulated categories with finitely many indecomposable objects, the Calabi-Yau dimension can be computed combinatorially, by finding the smallest d for which the Serre functor and the d'th power of the suspension functor have the same action on the Auslander-Reiten quiver. This is false, and we are grateful to Alex Dugas for pointing out a counterexample; see Section 5 of his paper arXiv:math/0808.1311 for more details. Unfortunately, we are not presently able to come up with a corrected version of the theorem, and this means that we cannot compute the Calabi-Yau dimensions of concrete stable module categories. Since these dimensions are necessary for identifying the categories with higher cluster categories, we presently have no means to achieve such identifications.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-02-19T13:43:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "18E30",
      "05E99",
      "16D50",
      "16G60",
      "16G70"
    ],
    "keywords": [
      "stable calabi-yau dimensions",
      "selfinjective algebras",
      "concrete stable module categories",
      "higher cluster categories",
      "theorem claims"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12451H"
    }
  }
}