{
  "id": "1704.06438",
  "version": "v1",
  "published": "2017-04-21T08:27:02.000Z",
  "updated": "2017-04-21T08:27:02.000Z",
  "title": "Quivers with relations for symmetrizable Cartan matrices V. Caldero-Chapoton formula",
  "authors": [
    "Christof Geiß",
    "Bernard Leclerc",
    "Jan Schröer"
  ],
  "comment": "24 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We generalize the Caldero-Chapoton formula for cluster algebras of finite type to the skew-symmetrizable case. This is done by replacing representation categories of Dynkin quivers by categories of locally free modules over certain Iwanaga-Gorenstein algebras introduced in Part I. The proof relies on the realization of the positive part of the enveloping algebra of a simple Lie algebra of the same finite type as a convolution algebra of constructible functions on representation varieties of $H$, given in Part III. Along the way, we obtain a new result on the PBW basis of this convolution algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-21T08:27:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F60",
      "16G20"
    ],
    "keywords": [
      "symmetrizable cartan matrices",
      "caldero-chapoton formula",
      "finite type",
      "convolution algebra",
      "simple lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}