{
  "id": "1608.08514",
  "version": "v1",
  "published": "2016-08-30T15:43:44.000Z",
  "updated": "2016-08-30T15:43:44.000Z",
  "title": "The homotopy category for gentle algebras",
  "authors": [
    "Raphael Bennett-Tennenhaus"
  ],
  "comment": "28 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We consider possibly infinite dimensional gentle algebras defined by taking the completion a locally-gentle algebra with respect to the arrow ideal. We show the unbounded homotopy category of finitely generated projective modules satisfies the Krull-Remak-Schmidt property, and that complexes here are direct sums of string and band complexes. The aim of this work is to investigate new situations one may adapt a classification technique, sometimes called the functorial filtration method. The name refers to the construction of certain functorially defined filtrations which are used in proving correctness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-30T15:43:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "homotopy category",
      "generated projective modules satisfies",
      "possibly infinite dimensional gentle algebras",
      "functorial filtration method",
      "locally-gentle algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}