{
  "id": "0909.4100",
  "version": "v2",
  "published": "2009-09-23T16:14:44.000Z",
  "updated": "2009-11-19T18:50:33.000Z",
  "title": "Quivers with potentials associated to triangulated surfaces, Part II: Arc representations",
  "authors": [
    "Daniel Labardini-Fragoso"
  ],
  "comment": "51 pages; 37 figures. v2: 52 pages, 37 figures; a reference added; proof of Corollary 6.7 added; minor editorial changes",
  "categories": [
    "math.RT"
  ],
  "abstract": "This paper is a representation-theoretic extension of Part I. It has been inspired by three recent developments: surface cluster algebras studied by Fomin-Shapiro-Thurston, the mutation theory of quivers with potentials initiated by Derksen-Weyman-Zelevinsky, and string modules associated to arcs on unpunctured surfaces by Assem-Brustle-Charbonneau-Plamondon. Modifying the latter construction, to each arc and each ideal triangulation of a bordered marked surface we associate in an explicit way a representation of the quiver with potential constructed in Part I, so that whenever two ideal triangulations are related by a flip, the associated representations are related by the corresponding mutation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-11-19T18:50:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "57M20"
    ],
    "keywords": [
      "arc representations",
      "triangulated surfaces",
      "potentials",
      "ideal triangulation",
      "surface cluster algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.4100L"
    }
  }
}