{
  "id": "1806.03540",
  "version": "v1",
  "published": "2018-06-09T20:56:56.000Z",
  "updated": "2018-06-09T20:56:56.000Z",
  "title": "Rational series in the free group and the Connes operator",
  "authors": [
    "Aaron Lauve",
    "Christophe Reutenauer"
  ],
  "comment": "22 pages, 2 figures",
  "journal": "Noncommutative birational geometry, representations and combinatorics, pp. 177-197, Contemp. Math., v. 592, Amer. Math. Soc., Providence, RI, 2013",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "We characterize rational series over the free group by using an operator introduced by A. Connes. We prove that rational Malcev--Neumann series posses rational expressions without simplifications. Finally, we develop an effective algorithm for solving the word problem in the free skew field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-09T20:56:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E05",
      "03D05",
      "13F25",
      "16S10"
    ],
    "keywords": [
      "free group",
      "connes operator",
      "rational malcev-neumann series posses rational",
      "malcev-neumann series posses rational expressions",
      "free skew field"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}