{
  "id": "1509.01861",
  "version": "v1",
  "published": "2015-09-06T22:04:15.000Z",
  "updated": "2015-09-06T22:04:15.000Z",
  "title": "Completely positive entropy actions of sofic groups with $\\mathbb{Z}$ in their center",
  "authors": [
    "Peter Burton"
  ],
  "comment": "24 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $\\Gamma$ be a sofic group with a copy of $\\mathbb{Z}$ in its center. We construct an uncountable family of pairwise nonisomorphic measure-preserving $\\Gamma$ actions with completely positive entropy, none of which is a factor of a Bernoulli shift. Our construction shows that the relation of isomorphism among completely positive entropy $\\Gamma$ actions is not smooth, in contrast with the relation of isomorphism among Bernoulli shifts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-06T22:04:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A35",
      "22F10",
      "28D15",
      "28D20"
    ],
    "keywords": [
      "positive entropy actions",
      "sofic group",
      "bernoulli shift",
      "isomorphism",
      "pairwise nonisomorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150901861B"
    }
  }
}