{
  "id": "1808.07317",
  "version": "v1",
  "published": "2018-08-22T11:26:35.000Z",
  "updated": "2018-08-22T11:26:35.000Z",
  "title": "Blocks with normal abelian defect and abelian p' inertial quotient",
  "authors": [
    "David Benson",
    "Radha Kessar",
    "Markus Linckelmann"
  ],
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "Let $k$ be an algebraically closed field of characteristic $p$, and let $\\mathcal{O}$ be either $k$ or its ring of Witt vectors $W(k)$. Let $G$ a finite group and $B$ a block of $\\mathcal{O}G$ with normal abelian defect group and abelian $p'$ inertial quotient. We show that $B$ is isomorphic to its second Frobenius twist. This is motivated by the fact that bounding Frobenius numbers is one of the key steps towards Donovan's conjecture. For $\\mathcal{O}=k$, we give an explicit description of the basic algebra of $B$ as a quiver with relations. It is a quantised version of the group algebra of the semidirect product $P\\rtimes L$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-22T11:26:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C20",
      "20J06"
    ],
    "keywords": [
      "inertial quotient",
      "normal abelian defect group",
      "second frobenius twist",
      "witt vectors",
      "semidirect product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}