{
  "id": "1506.02410",
  "version": "v1",
  "published": "2015-06-08T09:25:01.000Z",
  "updated": "2015-06-08T09:25:01.000Z",
  "title": "The derived category of surface algebras: the case of torus with one boundary component",
  "authors": [
    "Claire Amiot"
  ],
  "comment": "22 pages",
  "categories": [
    "math.RT",
    "math.AT"
  ],
  "abstract": "In this paper we refine the main result of a previous paper of the author with Grimeland on derived invariants of surface algebras. We restrict to the case where the surface is a torus with one boundary component and give an easily computable derived invariant for such surface algebras. This result permits to give answers to open questions on gentle algebras: it provides examples of gentle algebras with the same AG-invariant (in the sense of Avella-Alaminos and Geiss) that are not derived equivalent and gives a partial positive answer to a conjecture due to Bobi\\'nski and Malicki on gentle $2$-cycles algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-08T09:25:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E35",
      "16G20",
      "14F35",
      "13F60"
    ],
    "keywords": [
      "surface algebras",
      "boundary component",
      "derived category",
      "gentle algebras",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150602410A"
    }
  }
}