{
  "id": "2005.02223",
  "version": "v1",
  "published": "2020-05-05T14:25:08.000Z",
  "updated": "2020-05-05T14:25:08.000Z",
  "title": "A $9$-dimensional algebra which is not a block of a finite group",
  "authors": [
    "Markus Linckelmann",
    "William Murphy"
  ],
  "comment": "10 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We rule out a certain $9$-dimensional algebra over an algebraically closed field to be the basic algebra of a block of a finite group, thereby completing the classification of basic algebras of dimension at most $12$ of blocks of finite group algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-05T14:25:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dimensional algebra",
      "basic algebra",
      "finite group algebras",
      "classification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}