{
  "id": "1412.6405",
  "version": "v1",
  "published": "2014-12-19T16:03:04.000Z",
  "updated": "2014-12-19T16:03:04.000Z",
  "title": "Rigid and Schurian modules over cluster-tilted algebras of tame type",
  "authors": [
    "Robert J. Marsh",
    "Idun Reiten"
  ],
  "comment": "39 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We give an example of a cluster-tilted algebra $\\Lambda$ with quiver Q, such that the associated cluster algebra A(Q) has a denominator vector which is not the dimension vector of any indecomposable $\\Lambda$-module. This answers a question posed by T. Nakanishi. The relevant example is a cluster-tilted algebra associated with a tame hereditary algebra. We show that for such a cluster-tilted algebra $\\Lambda$, we can write any denominator vector as a sum of the dimension vectors of at most three indecomposable rigid $\\Lambda$-modules. In order to do this it is necessary, and of independent interest, to first classify the indecomposable rigid $\\Lambda$-modules in this case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-19T16:03:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F60",
      "16G20",
      "16G70",
      "18E30"
    ],
    "keywords": [
      "cluster-tilted algebra",
      "tame type",
      "schurian modules",
      "dimension vector",
      "denominator vector"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.6405M"
    }
  }
}