{
  "id": "math/0408291",
  "version": "v1",
  "published": "2004-08-22T00:57:31.000Z",
  "updated": "2004-08-22T00:57:31.000Z",
  "title": "Crossed products by minimal homeomorphisms",
  "authors": [
    "Huaxin Lin",
    "N. Christopher Phillips"
  ],
  "comment": "AMSLaTeX; 24 pages, no figures",
  "categories": [
    "math.OA"
  ],
  "abstract": "Let X be an infinite compact metric space with finite covering dimension and let h be a minimal homeomorphism of X. Let A be the associated crossed product C*-algebra. We show that A has tracial rank zero whenever the image of K_0 (A) in the affine functions on the tracial state space of A is dense. As a consequence, we show that these crossed product C*-algebras are in fact simple AH algebras with real rank zero. When X is connected and h is further assumed to be uniquely ergodic, then the above happens if and only if the rotation number associated to h has irrational values. By applying the classification theorem for nuclear simple C*-algebras with tracial rank zero, we show that two such dynamical systems have isomorphic crossed products if and only if they have isomorphic scaled ordered K-theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-08-22T00:57:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L55"
    ],
    "keywords": [
      "crossed product",
      "minimal homeomorphism",
      "tracial rank zero",
      "infinite compact metric space",
      "fact simple ah algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8291L"
    }
  }
}