{
  "id": "math/0411341",
  "version": "v5",
  "published": "2004-11-15T20:23:37.000Z",
  "updated": "2005-09-27T13:45:18.000Z",
  "title": "Cluster algebras of finite type and positive symmetrizable matrices",
  "authors": [
    "Michael Barot",
    "Christof Geiss",
    "Andrei Zelevinsky"
  ],
  "comment": "20 pages. In version 3, some new material is added in the end of section 2, discussing the classification and characterizations of positive quasi-Cartan matrices. In final version 4, Proposition 2.9 is corrected and its proof expanded. To appear in J. London Math. Soc. In version 5 only typos in the arXiv data fixed",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "The paper is motivated by an analogy between cluster algebras and Kac-Moody algebras: both theories share the same classification of finite type objects by familiar Cartan-Killing types. However the underlying combinatorics beyond the two classifications is different: roughly speaking, Kac-Moody algebras are associated with (symmetrizable) Cartan matrices, while cluster algebras correspond to skew-symmetrizable matrices. We study an interplay between the two classes of matrices, in particular, establishing a new criterion for deciding whether a given skew-symmetrizable matrix gives rise to a cluster algebra of finite type.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2005-09-27T13:45:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive symmetrizable matrices",
      "kac-moody algebras",
      "finite type objects",
      "cluster algebras correspond",
      "theories share"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....11341B"
    }
  }
}