{
  "id": "math/0607151",
  "version": "v1",
  "published": "2006-07-06T09:50:37.000Z",
  "updated": "2006-07-06T09:50:37.000Z",
  "title": "A geometric description of $m$-cluster categories",
  "authors": [
    "Karin Baur",
    "Robert J. Marsh"
  ],
  "comment": "14 pages, 5 figures",
  "journal": "Trans. Amer. Math. Soc. 360 (2008), 5789-5803",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We show that the $m$-cluster category of type $A_{n-1}$ is equivalent to a certain geometrically-defined category of diagonals of a regular $nm+2$-gon. This generalises a result of Caldero, Chapoton and Schiffler for $m=1$. The approach uses the theory of translation quivers and their corresponding mesh categories. We also introduce the notion of the $m$th power of a translation quiver and show how it can be used to realise the $m$-cluster category in terms of the cluster category.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-07-06T09:50:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16G70",
      "18E30"
    ],
    "keywords": [
      "cluster category",
      "geometric description",
      "translation quiver",
      "corresponding mesh categories",
      "th power"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Trans. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7151B"
    }
  }
}