{
  "id": "0812.0650",
  "version": "v3",
  "published": "2008-12-03T04:42:10.000Z",
  "updated": "2010-01-08T03:21:16.000Z",
  "title": "Cluster-tilted algebras of type $D_n$",
  "authors": [
    "Wenxu Ge",
    "Hongbo Lv",
    "Shunhua Zhang"
  ],
  "comment": "21 pages, 13 figures, accepted for publication in Comm.Algebra",
  "journal": "Comm.Algebra, 38(7)(2010), 2418-2432",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Let $H$ be a hereditary algebra of Dynkin type $D_n$ over a field $k$ and $\\mathscr{C}_H$ be the cluster category of $H$. Assume that $n\\geq 5$ and that $T$ and $T'$ are tilting objects in $\\mathscr{C}_H$. We prove that the cluster-tilted algebra $\\Gamma=\\mathrm{End}_{\\mathscr{C}_H}(T)^{\\rm op}$ is isomorphic to $\\Gamma'=\\mathrm{End}_{\\mathscr{C}_H}(T')^{\\rm op}$ if and only if $T=\\tau^iT'$ or $T=\\sigma\\tau^jT'$ for some integers $i$ and $j$, where $\\tau$ is the Auslander-Reiten translation and $\\sigma$ is the automorphism of $\\mathscr{C}_H$ defined in section 4.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-01-08T03:21:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16G70",
      "05E15"
    ],
    "keywords": [
      "cluster-tilted algebra",
      "hereditary algebra",
      "dynkin type",
      "cluster category",
      "auslander-reiten translation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.0650G"
    }
  }
}