{
  "id": "1312.3659",
  "version": "v2",
  "published": "2013-12-12T21:47:41.000Z",
  "updated": "2015-03-04T16:51:24.000Z",
  "title": "Lattice structure of torsion classes for path algebras",
  "authors": [
    "Osamu Iyama",
    "Idun Reiten",
    "Hugh Thomas",
    "Gordana Todorov"
  ],
  "comment": "10 pages. Minor errors are corrected, and references are updated in the second version",
  "categories": [
    "math.RT"
  ],
  "abstract": "We consider module categories of path algebras of connected acyclic quivers. It is shown in this paper that the set of functorially finite torsion classes form a lattice if and only if the quiver is either Dynkin quiver of type A, D, E, or the quiver has exactly two vertices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-12T21:47:41.000Z",
      "comment": "10 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-03-04T16:51:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "18E40",
      "05E10"
    ],
    "keywords": [
      "path algebras",
      "lattice structure",
      "functorially finite torsion classes form",
      "module categories",
      "connected acyclic quivers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.3659I"
    }
  }
}