{
  "id": "1012.2169",
  "version": "v3",
  "published": "2010-12-10T03:38:48.000Z",
  "updated": "2011-02-16T08:20:51.000Z",
  "title": "On the derivation algebra of the free Lie algebra and trace maps",
  "authors": [
    "Naoya Enomoto",
    "Takao Satoh"
  ],
  "comment": "40 pages. We add a link to our preprint in the reference [43]",
  "categories": [
    "math.GR",
    "math.RT"
  ],
  "abstract": "We calculate the irreducible decomposition of the images of the Johnson homomorphisms of the automorphism group of a free group and a free metabelian group. We determine the abelianization of the derivation algebra of the Chen Lie algebra as a Lie algebra, and show that the abelianizaton is given by the degree one part and the Morita's trace maps. We also consider twisted cohomology groups of the automorphism group of a free nilpotent group. We show that the trace map for the exterior product defines a non-trivial twisted second cohomology class of it.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-02-16T08:20:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F28",
      "17B40",
      "20G05"
    ],
    "keywords": [
      "free lie algebra",
      "derivation algebra",
      "automorphism group",
      "non-trivial twisted second cohomology class",
      "chen lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.2169E"
    }
  }
}