{
  "id": "math/0606182",
  "version": "v1",
  "published": "2006-06-08T10:13:17.000Z",
  "updated": "2006-06-08T10:13:17.000Z",
  "title": "Linear Representations of the Automorphism Group of a Free Group",
  "authors": [
    "Fritz Grunewald",
    "Alexander Lubotzky"
  ],
  "categories": [
    "math.GR",
    "math.RT"
  ],
  "abstract": "Let $F_n$ be the free group on $n\\ge 2$ elements and $\\A(F_n)$ its group of automorphisms. In this paper we present a rich collection of linear representations of $\\A(F_n)$ arising through the action of finite index subgroups of it on relation modules of finite quotient groups of $F_n$. We show (under certain conditions) that the images of our representations are arithmetic groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-08T10:13:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free group",
      "linear representations",
      "automorphism group",
      "finite quotient groups",
      "finite index subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6182G"
    }
  }
}