{
  "id": "2102.02104",
  "version": "v1",
  "published": "2021-02-03T15:18:04.000Z",
  "updated": "2021-02-03T15:18:04.000Z",
  "title": "The size of an exceptional sequence can be arbitrarily large",
  "authors": [
    "Hipolito Treffinger"
  ],
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "In this short note we show that the size of an exceptional sequence in the module category of a finite dimensional algebra $A$ can be arbitrarily large in comparison to the number of isomorphism classes of simple $A$-modules. We do so by constructing an exceptional sequence in the module category of the Auslander algebra of the path algebra of the linearly oriented $\\mathbb{A}_n$ quiver.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-03T15:18:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exceptional sequence",
      "arbitrarily large",
      "module category",
      "finite dimensional algebra",
      "short note"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}