{
  "id": "1604.04437",
  "version": "v1",
  "published": "2016-04-15T11:32:44.000Z",
  "updated": "2016-04-15T11:32:44.000Z",
  "title": "On blocks of defect two and one simple module, and Lie algebra structure of $HH^1$",
  "authors": [
    "David John Benson",
    "Radha Kessar",
    "Markus Linckelmann"
  ],
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "Let $k$ be a field of odd prime characteristic $p$. We calculate the Lie algebra structure of the first Hochschild cohomology of a class of quantum complete intersections over $k$. As a consequence, we prove that if $B$ is a defect $2$-block of a finite group algebra $kG$ whose Brauer correspondent $C$ has a unique isomorphism class of simple modules, then a basic algebra of $B$ is a local algebra which can be generated by at most $2\\sqrt I$ elements, where $I$ is the inertial index of $B$, and where we assume that $k$ is a splitting field for $B$ and $C$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-15T11:32:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C20"
    ],
    "keywords": [
      "lie algebra structure",
      "simple module",
      "quantum complete intersections",
      "first hochschild cohomology",
      "unique isomorphism class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160404437B"
    }
  }
}