{
  "id": "1401.7300",
  "version": "v3",
  "published": "2014-01-28T19:17:54.000Z",
  "updated": "2014-06-24T10:28:19.000Z",
  "title": "$C^\\ast$-simple groups without free subgroups",
  "authors": [
    "A. Yu. Olshanskii",
    "D. V. Osin"
  ],
  "categories": [
    "math.GR",
    "math.OA"
  ],
  "abstract": "We construct first examples of non-trivial groups without non-cyclic free subgroups whose reduced $C^\\ast$-algebra is simple and has unique trace. This answers a question of de la Harpe. Both torsion and torsion free examples are provided. In particular, we show that the reduced $C^\\ast$-algebra of the free Burnside group $B(m,n)$ of rank $m\\ge 2$ and any sufficiently large odd exponent $n$ is simple and has unique trace.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-06-24T10:28:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F06",
      "20F67",
      "22D25",
      "47L05"
    ],
    "keywords": [
      "simple groups",
      "unique trace",
      "non-cyclic free subgroups",
      "torsion free examples",
      "free burnside group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.7300O"
    }
  }
}