{
  "id": "math/0510251",
  "version": "v2",
  "published": "2005-10-12T14:56:19.000Z",
  "updated": "2006-04-12T14:56:31.000Z",
  "title": "From triangulated categories to cluster algebras II",
  "authors": [
    "Philippe Caldero",
    "Bernhard Keller"
  ],
  "comment": "23 pages. The proofs rely on a weaker version of positivity",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "In the acyclic case, we establish a one-to-one correspondence between the tilting objects of the cluster category and the clusters of the associated cluster algebra. This correspondence enables us to solve conjectures on cluster algebras. We prove a multiplicativity theorem, a denominator theorem, and some conjectures on properties of the mutation graph. As in the previous article, the proofs rely on the Calabi-Yau property of the cluster category.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-04-12T14:56:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "18E30"
    ],
    "keywords": [
      "triangulated categories",
      "cluster category",
      "denominator theorem",
      "one-to-one correspondence",
      "multiplicativity theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10251C"
    }
  }
}