{
  "id": "math/0511384",
  "version": "v2",
  "published": "2005-11-15T14:25:01.000Z",
  "updated": "2006-06-19T13:05:54.000Z",
  "title": "Applications of BGP-reflection functors: isomorphisms of cluster algebras",
  "authors": [
    "Bin Zhu"
  ],
  "comment": "revised version",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Given a symmetrizable generalized Cartan matrix $A$, for any index $k$, one can define an automorphism associated with $A,$ of the field $\\mathbf{Q}(u_1, >..., u_n)$ of rational functions of $n$ independent indeterminates $u_1,..., u_n.$ It is an isomorphism between two cluster algebras associated to the matrix $A$ (see section 4 for precise meaning). When $A$ is of finite type, these isomorphisms behave nicely, they are compatible with the BGP-reflection functors of cluster categories defined in [Z1, Z2] if we identify the indecomposable objects in the categories with cluster variables of the corresponding cluster algebras, and they are also compatible with the \"truncated simple reflections\" defined in [FZ2, FZ3]. Using the construction of preprojective or preinjective modules of hereditary algebras by Dlab-Ringel [DR] and the Coxeter automorphisms (i.e., a product of these isomorphisms), we construct infinitely many cluster variables for cluster algebras of infinite type and all cluster variables for finite types.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-06-19T13:05:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16G70"
    ],
    "keywords": [
      "bgp-reflection functors",
      "isomorphism",
      "cluster variables",
      "applications",
      "truncated simple reflections"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s11425-006-2004-6",
      "journal": "Science in China A: Mathematics",
      "year": 2006,
      "month": "Dec",
      "volume": 49,
      "number": 12,
      "pages": 1839
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006ScChA..49.1839Z"
    }
  }
}