{
  "id": "1707.02738",
  "version": "v1",
  "published": "2017-07-10T08:26:12.000Z",
  "updated": "2017-07-10T08:26:12.000Z",
  "title": "Cartan subgroups and regular points of o-minimal groups",
  "authors": [
    "Elias Baro",
    "Alessandro Berarducci",
    "Margarita Otero"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Let G be a group definable in an o-minimal structure M. We prove that the union of the Cartan subgroups of G is a dense subset of G. When M is an expansion of a real closed field we give a characterization of Cartan subgroups of G via their Lie algebras which allow us to prove firstly, that every Cartan subalgebra of the Lie algebra of G is the Lie algebra of a definable subgroup - a Cartan subgroup of G -, and secondly, that the set of regular points of G - a dense subset of G - is formed by points which belong to a unique Cartan subgroup of G.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-10T08:26:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C64",
      "20G15",
      "20E34"
    ],
    "keywords": [
      "regular points",
      "o-minimal groups",
      "lie algebra",
      "dense subset",
      "unique cartan subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}