{
  "id": "1507.07524",
  "version": "v1",
  "published": "2015-07-27T18:49:29.000Z",
  "updated": "2015-07-27T18:49:29.000Z",
  "title": "A Criterion for $\\mathcal{Z}$-Stability with Applications to Crossed Products",
  "authors": [
    "Julian Buck",
    "Aaron Tikuisis"
  ],
  "comment": "6 pages",
  "categories": [
    "math.OA"
  ],
  "abstract": "Building on an argument by Toms and Winter, we show that if $A$ is a simple, separable, unital, $\\mathcal{Z}$-stable C*-algebra, then the crossed product of $C(X,A)$ by an automorphism is also Z-stable, provided that the automorphism induces a minimal homeomorphism on $X$. As a consequence, we observe that if $A$ is nuclear and purely infinite then the crossed product is a Kirchberg algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-27T18:49:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "crossed product",
      "applications",
      "automorphism induces",
      "kirchberg algebra",
      "minimal homeomorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150707524B"
    }
  }
}