{
  "id": "1708.02468",
  "version": "v1",
  "published": "2017-08-08T12:45:12.000Z",
  "updated": "2017-08-08T12:45:12.000Z",
  "title": "On universal minimal proximal flows of topological groups",
  "authors": [
    "Xiongping Dai",
    "Eli Glasner"
  ],
  "comment": "14 pages. Comments are welcome",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we show that the action of a characteristically simple, non-extremely amenable (non-strongly amenable, non-amenable) group on its universal minimal (minimal proximal, minimal strongly proximal) flow is effective. We present necessary and sufficient conditions, for the action of a topological group with trivial center on its universal minimal proximal flow, to be effective. A theorem of Furstenberg about the isomorphism of the universal minimal proximal flows of a discrete group and its subgroups of finite index ([Theorem~II.4.4]) is strengthened. Finally, for a pair of groups $H < G$ the same method is applied in order to extend the action of $H$ on its universal minimal proximal flow to an action of its commensurator group $\\mathrm{Comm}_G(H)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-08T12:45:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05"
    ],
    "keywords": [
      "universal minimal proximal flow",
      "topological group",
      "finite index",
      "commensurator group",
      "trivial center"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}