{
  "id": "2004.11136",
  "version": "v1",
  "published": "2020-04-23T13:32:45.000Z",
  "updated": "2020-04-23T13:32:45.000Z",
  "title": "A geometric model for the module category of a skew-gentle algebra",
  "authors": [
    "Ping He",
    "Yu Zhou",
    "Bin Zhu"
  ],
  "comment": "38 pages, 24 figures",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "In this article, we realize skew-gentle algebras as skew-tiling algebras associated to admissible partial triangulations of punctured marked surfaces. Based on this, we establish a bijection between tagged permissible curves and certain indecomposable modules, interpret the Auslander-Reiten translation via the tagged rotation, and show intersection-dimension formulas. As an application, we classify support $\\tau$-tilting modules for skew-gentle algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-23T13:32:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "module category",
      "geometric model",
      "admissible partial triangulations",
      "realize skew-gentle algebras",
      "auslander-reiten translation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}