{
  "id": "math/0608727",
  "version": "v1",
  "published": "2006-08-29T18:45:04.000Z",
  "updated": "2006-08-29T18:45:04.000Z",
  "title": "$m$-cluster categories and $m$-replicated algebras",
  "authors": [
    "I. Assem",
    "T. Brüstle",
    "R. Schiffler",
    "G. Todorov"
  ],
  "comment": "28 pages, 2 figures",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Let A be a hereditary algebra over an algebraically closed field. We prove that an exact fundamental domain for the m-cluster category of A is the m-left part of the m-replicated algebra $A^{(m)}$ of A. Moreover, we obtain a one-to-one correspondence between the tilting objects in the m-cluster category (that is, the m-clusters) and those tilting $A^{(m)}$-modules for which all non projective-injective direct summands lie in the m-left part of $A^{(m)}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-08-29T18:45:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16G70",
      "16E10",
      "18E30"
    ],
    "keywords": [
      "cluster categories",
      "replicated algebras",
      "m-cluster category",
      "non projective-injective direct summands lie",
      "m-left part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8727A"
    }
  }
}