{
  "id": "2206.03911",
  "version": "v1",
  "published": "2022-06-08T14:06:38.000Z",
  "updated": "2022-06-08T14:06:38.000Z",
  "title": "The Grothendieck Groups of Discrete Cluster Categories of Dynkin Type $A_{\\infty}$",
  "authors": [
    "Dave Murphy"
  ],
  "comment": "18 pages",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "In this work we compute the triangulated Grothendieck groups for each of the family of discrete cluster categories of Dynkin type $A_{\\infty}$ as introduced by Holm-Jorgensen. Subsequently, we also compute the Grothendieck group of a completion of these discrete cluster categories in the sense of Paquette-Yildirim.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-08T14:06:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete cluster categories",
      "dynkin type",
      "triangulated grothendieck groups",
      "holm-jorgensen"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}