{
  "id": "1708.07419",
  "version": "v1",
  "published": "2017-08-22T20:13:56.000Z",
  "updated": "2017-08-22T20:13:56.000Z",
  "title": "Undecidability of Equations in Free Lie Algebras",
  "authors": [
    "Olga Kharlampovich",
    "Alexei Myasnikov"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1606.03617",
  "categories": [
    "math.LO",
    "math.RA"
  ],
  "abstract": "In this paper we prove undecidability of finite systems of equations in free Lie algebras of rank at least three over an arbitrary field. We show that the ring of integers $\\mathbb{Z}$ is interpretable by positive existential formulas in such free Lie algebras over a field of characteristic zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-22T20:13:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C60"
    ],
    "keywords": [
      "free lie algebras",
      "undecidability",
      "characteristic zero",
      "arbitrary field",
      "positive existential formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}