{
  "id": "0809.0074",
  "version": "v1",
  "published": "2008-08-30T17:03:50.000Z",
  "updated": "2008-08-30T17:03:50.000Z",
  "title": "Group algebras of finite groups as Lie algebras",
  "authors": [
    "Ivan Marin"
  ],
  "comment": "12 pages",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a decomposition in simple factors of these Lie algebras, in terms of the ordinary representations of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-30T17:03:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "17B99"
    ],
    "keywords": [
      "group algebra",
      "finite group",
      "natural lie algebra structure",
      "ordinary representations",
      "simple factors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.0074M"
    }
  }
}