{
  "id": "1712.00823",
  "version": "v1",
  "published": "2017-12-03T19:35:16.000Z",
  "updated": "2017-12-03T19:35:16.000Z",
  "title": "Approaching the UCT problem via crossed products of the Razak-Jacelon algebra",
  "authors": [
    "Selçuk Barlak",
    "Gábor Szabó"
  ],
  "comment": "10 pages",
  "categories": [
    "math.OA"
  ],
  "abstract": "We show that the UCT problem for separable, nuclear $\\mathrm C^*$-algebras relies only on whether the UCT holds for crossed products of certain finite cyclic group actions on the Razak-Jacelon algebra. This observation is analogous to and in fact recovers a characterization of the UCT problem in terms of finite group actions on the Cuntz algebra $\\mathcal O_2$ established in previous work by the authors. Although based on a similar approach, the new conceptual ingredients in the finite context are the recent advances in the classification of stably projectionless $\\mathrm C^*$-algebras, as well as a known characterization of the UCT problem in terms of certain tracially AF $\\mathrm C^*$-algebras due to Dadarlat.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-03T19:35:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uct problem",
      "razak-jacelon algebra",
      "crossed products",
      "finite cyclic group actions",
      "finite group actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}