{
  "id": "1201.4833",
  "version": "v2",
  "published": "2012-01-23T19:40:26.000Z",
  "updated": "2012-09-06T13:34:24.000Z",
  "title": "On the Auslander-Reiten quiver of the representations of an infinite quiver",
  "authors": [
    "Charles Paquette"
  ],
  "comment": "28 pages, 1 figure",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let Q be a strongly locally finite quiver and denote by rep(Q) the category of locally finite dimensional representations of Q over some fixed field k. The main purpose of this paper is to get a better understanding of rep(Q) by means of its Auslander-Reiten quiver. To achieve this goal, we define a category C(Q) which is a full, abelian and Hom-finite subcategory of rep(Q) containing all the almost split sequences of rep(Q). We give a complete description of the Auslander-Reiten quiver of C(Q) by describing its connected components. Finally, we prove that these connected components are also connected components of the Auslander-Reiten quiver of rep(Q). We end the paper by giving a conjecture describing the Auslander-Reiten components of rep(Q) that cannot be obtained as Auslander-Reiten components of C(Q).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-06T13:34:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16G70"
    ],
    "keywords": [
      "auslander-reiten quiver",
      "infinite quiver",
      "connected components",
      "auslander-reiten components",
      "locally finite dimensional representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.4833P"
    }
  }
}