{
  "id": "1502.06489",
  "version": "v1",
  "published": "2015-02-23T16:29:44.000Z",
  "updated": "2015-02-23T16:29:44.000Z",
  "title": "A geometric realization of tame categories",
  "authors": [
    "Karin Baur",
    "Hermund André Torkildsen"
  ],
  "comment": "36 pages, many figures",
  "categories": [
    "math.RT"
  ],
  "abstract": "We give a geometric realization of module categories of type $\\tilde{A}_n$. We work with oriented arcs to define a translation quiver isomorphic to the Auslander-Reiten quiver of the module category of type $\\tilde{A}_n$. To get a description of the module category, we introduce long moves between arcs. These allow us to include the infinite radical in the geometric description. Finally, our results can also be used to describe the corresponding cluster categories by taking unoriented arcs instead.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-23T16:29:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric realization",
      "tame categories",
      "module category",
      "translation quiver isomorphic",
      "corresponding cluster categories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}