{
  "id": "1202.5698",
  "version": "v1",
  "published": "2012-02-25T21:07:56.000Z",
  "updated": "2012-02-25T21:07:56.000Z",
  "title": "Modules over cluster-tilted algebras determined by their dimension vectors",
  "authors": [
    "Ibrahim Assem",
    "Grégoire Dupont"
  ],
  "comment": "9 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We prove that indecomposable transjective modules over cluster-tilted algebras are uniquely determined by their dimension vectors. Similarly, we prove that for cluster-concealed algebras, rigid modules lifting to rigid objects in the corresponding cluster category are uniquely determined by their dimension vectors. Finally, we apply our results to a conjecture of Fomin and Zelevinsky on denominators of cluster variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-25T21:07:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "13F60"
    ],
    "keywords": [
      "dimension vectors",
      "cluster-tilted algebras",
      "cluster variables",
      "corresponding cluster category",
      "rigid objects"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.5698A"
    }
  }
}