{
  "id": "math/0703540",
  "version": "v3",
  "published": "2007-03-19T06:03:08.000Z",
  "updated": "2010-06-16T06:59:12.000Z",
  "title": "Cluster characters for triangulated 2-Calabi--Yau categories",
  "authors": [
    "Yann Palu"
  ],
  "comment": "21 pages. The numberings now coincide with those of the published version",
  "journal": "Annales de l'Institut Fourier Tome 58, 6 (2008) 2221-2248",
  "categories": [
    "math.RT",
    "math.CT",
    "math.RA"
  ],
  "abstract": "Starting from an arbitrary cluster-tilting object $T$ in a 2-Calabi--Yau category over an algebraically closed field, as in the setting of Keller and Reiten, we define, for each object $L$, a fraction $X(T,L)$ using a formula proposed by Caldero and Keller. We show that the map taking $L$ to $X(T,L)$ is a cluster character, i.e. that it satisfies a certain multiplication formula. We deduce that it induces a bijection, in the finite and the acyclic case, between the indecomposable rigid objects of the cluster category and the cluster variables, which confirms a conjecture of Caldero and Keller.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-06-16T06:59:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cluster character",
      "cluster variables",
      "arbitrary cluster-tilting object",
      "acyclic case"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3540P"
    }
  }
}