{
  "id": "math/0506018",
  "version": "v2",
  "published": "2005-06-01T13:08:38.000Z",
  "updated": "2005-06-11T18:08:46.000Z",
  "title": "From triangulated categories to cluster algebras",
  "authors": [
    "Philippe Caldero",
    "Bernhard Keller"
  ],
  "comment": "31 pages, typos corrected",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra A of finite type can be realized as a Hall algebra, called the exceptional Hall algebra, of the cluster category. This realization provides a natural basis for A. We prove new results and formulate conjectures on `good basis' properties, positivity, denominator theorems and toric degenerations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-06-11T18:08:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "18E30"
    ],
    "keywords": [
      "cluster algebra",
      "triangulated category",
      "cluster category",
      "exceptional hall algebra",
      "finite type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......6018C"
    }
  }
}