{
  "id": "1112.5896",
  "version": "v1",
  "published": "2011-12-26T21:45:15.000Z",
  "updated": "2011-12-26T21:45:15.000Z",
  "title": "Fundamental domains of cluster categories inside module categories",
  "authors": [
    "Juan Ángel Cappa",
    "Maria Inés Platzeck",
    "Idun Reiten"
  ],
  "comment": "20 pages, 9 figures",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $H$ be a finite dimensional hereditary algebra over an algebraically closed field, and let $\\mathcal{C}_{H}$ be the corresponding cluster category. We give a description of the (standard) fundamental domain of $\\mathcal{C}_{H} $ in the bounded derived category $\\mathcal{D}^{b}(H)$, and of the cluster-tilting objects, in terms of the category $\\mod\\Gamma $\\ of finitely generated modules over a suitable tilted algebra $% \\Gamma .$ Furthermore, we apply this description to obtain (the quiver of) an arbitrary cluster-tilted algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-26T21:45:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16G70",
      "18E30"
    ],
    "keywords": [
      "cluster categories inside module categories",
      "fundamental domain",
      "finite dimensional hereditary algebra",
      "corresponding cluster category",
      "description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.5896A"
    }
  }
}