{
  "id": "math/0408330",
  "version": "v1",
  "published": "2004-08-24T13:25:55.000Z",
  "updated": "2004-08-24T13:25:55.000Z",
  "title": "Extending representations of braid groups to the automorphism groups of free groups",
  "authors": [
    "Valerij G. Bardakov"
  ],
  "comment": "14 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We construct a linear representation of the group IA(F_n) of IA-automorphisms of a free group F_n, an extension of the Gassner representation of the pure braid group P_n. Although the problem of faithfulness of the Gassner representation is still open for n > 3, we prove that the restriction of our representation to the group of basis conjugating automorphisms Cb_n contains a non-trivial kernel even if n=2. We construct also an extensions of the Burau representation to the group of conjugating automorphisms C_n. This representation is not faithful for n > 1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-08-24T13:25:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20E05",
      "20F28",
      "20G15"
    ],
    "keywords": [
      "free group",
      "automorphism groups",
      "extending representations",
      "gassner representation",
      "pure braid group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8330B"
    }
  }
}