{
  "id": "1704.04939",
  "version": "v1",
  "published": "2017-04-17T11:54:13.000Z",
  "updated": "2017-04-17T11:54:13.000Z",
  "title": "Cartan subalgebras and the UCT problem, II",
  "authors": [
    "Selcuk Barlak",
    "Xin Li"
  ],
  "comment": "26 pages",
  "categories": [
    "math.OA",
    "math.KT"
  ],
  "abstract": "We show that outer approximately represenbtable actions of a finite cyclic group on UCT Kirchberg algebras satisfy a certain quasi-freeness type property if the corresponding crossed products satisfy the UCT and absorb a suitable UHF algebra tensorially. More concretely, we prove that for such an action there exists an inverse semigroup of homogeneous partial isometries that generates the ambient C*-algebra and whose idempotent semilattice generates a Cartan subalgebra. We prove a similar result for actions of finite cyclic groups with the Rokhlin property on UCT Kirchberg algebras absorbing a suitable UHF algebra. These results rely on a new construction of Cartan subalgebras in certain inductive limits of Cartan pairs. We also provide a characterisation of the UCT problem in terms of finite order automorphisms, Cartan subalgebras and inverse semigroups of partial isometries of the Cuntz algebra $\\mathcal{O}_2$. This generalizes earlier work of the authors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-17T11:54:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L05",
      "46L40",
      "46L80",
      "19K35"
    ],
    "keywords": [
      "cartan subalgebra",
      "uct problem",
      "finite cyclic group",
      "suitable uhf algebra",
      "uct kirchberg algebras satisfy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}