{
  "id": "1402.1260",
  "version": "v1",
  "published": "2014-02-06T06:32:25.000Z",
  "updated": "2014-02-06T06:32:25.000Z",
  "title": "Lattice structure of torsion classes for hereditary artin algebras",
  "authors": [
    "Claus Michael Ringel"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let A be a connected hereditary artin algebra. We show that the set of functorially finite torsion classes of A-modules is a lattice if and only if A is either representation-finite (thus a Dynkin algebra) or A has only two simple modules. For the case of A being the path algebra of a quiver, this result has recently been established by Iyama-Reiten-Thomas-Todorov and our proof follows closely their considerations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-06T06:32:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lattice structure",
      "functorially finite torsion classes",
      "connected hereditary artin algebra",
      "dynkin algebra",
      "simple modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.1260R"
    }
  }
}