{
  "id": "1609.09688",
  "version": "v1",
  "published": "2016-09-30T12:07:08.000Z",
  "updated": "2016-09-30T12:07:08.000Z",
  "title": "Mapping cones in the bounded derived category of a gentle algebra",
  "authors": [
    "Ilke Canakci",
    "David Pauksztello",
    "Sibylle Schroll"
  ],
  "comment": "34 pages, many figures",
  "categories": [
    "math.RT",
    "math.AG"
  ],
  "abstract": "Gentle algebras are a class of algebras that are derived tame. They therefore provide a concrete setting to study the structure of the (bounded) derived category in detail. In this article we explicitly describe the triangulated structure of the bounded derived category of a gentle algebra by describing its triangles. In particular, we develop a graphical calculus which gives the indecomposable summands of the mapping cones of morphisms in a canonical basis of the Hom-space between any two indecomposable complexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-30T12:07:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "16G10",
      "05E10"
    ],
    "keywords": [
      "bounded derived category",
      "gentle algebra",
      "mapping cones",
      "derived tame",
      "triangulated structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}