{
  "id": "1502.06275",
  "version": "v1",
  "published": "2015-02-22T22:03:48.000Z",
  "updated": "2015-02-22T22:03:48.000Z",
  "title": "Combinatorial Restrictions on the Tree Class of the Auslander-Reiten Quiver of a Triangulated Category",
  "authors": [
    "Kosmas Diveris",
    "Marju Purin",
    "Peter Webb"
  ],
  "categories": [
    "math.RT",
    "math.CO",
    "math.KT",
    "math.RA"
  ],
  "abstract": "We show that if a connected, Hom-finite, Krull-Schmidt triangulated category has an Auslander-Reiten quiver component with Dynkin tree class then the category has Auslander-Reiten triangles and that component is the entire quiver. This is an analogue for triangulated categories of a theorem of Auslander, and extends a previous result of Scherotzke. We also show that if there is a quiver component with extended Dynkin tree class, then other components must also have extended Dynkin class or one of a small set of infinite trees, provided there is a non-zero homomorphism between the components. The proofs use the theory of additive functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-22T22:03:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G70",
      "18E30",
      "16E35",
      "13F60"
    ],
    "keywords": [
      "triangulated category",
      "combinatorial restrictions",
      "auslander-reiten quiver component",
      "extended dynkin tree class",
      "non-zero homomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}