{
  "id": "1912.04367",
  "version": "v1",
  "published": "2019-12-09T20:46:52.000Z",
  "updated": "2019-12-09T20:46:52.000Z",
  "title": "Derived equivalences between skew-gentle algebras using orbifolds",
  "authors": [
    "Claire Amiot",
    "Thomas Brüstle"
  ],
  "comment": "46 pages",
  "categories": [
    "math.RT",
    "math.SG"
  ],
  "abstract": "Skew-gentle algebras are skew-group algebras of gentle algebras equipped with a certain $\\Z_2$-action. Building on the bijective correspondence between gentle algebras and dissected surfaces, we obtain in this paper a bijection between skew-gentle algebras and certain dissected orbifolds that admit a double cover. We prove the compatibility of the $\\Z_2$-action on the double cover with the skew-group algebra construction. This allows us to investigate the derived equivalence relation between skew-gentle algebras in geometric terms: We associate to each skew-gentle algebra a line field on the orbifold, and on its double cover, and interpret different kinds of derived equivalences of skew-gentle algebras in terms of diffeomorphisms respecting the homotopy class of the line fields associated to the algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-09T20:46:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16E35",
      "57R18"
    ],
    "keywords": [
      "skew-gentle algebra",
      "double cover",
      "gentle algebras",
      "line field",
      "skew-group algebra construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}