JournalsjncgVol. 9, No. 4pp. 1383–1393

The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras

  • Selçuk Barlak

    University of Southern Denmark, Odense, Denmark
  • Dominic Enders

    University of Copenhagen, Denmark
  • Hiroki Matui

    Chiba University, Japan
  • Gábor Szabó

    Westfälische Wilhelms-Universität Münster, Germany
  • Wilhelm Winter

    Westfälische Wilhelms-Universität Münster, Germany
The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras cover

Abstract

We investigate outer symmetries on unital Kirchberg algebras with respect to the Rokhlin property and finite Rokhlin dimension. In stark contrast to the restrictiveness of the Rokhlin property, every such action has Rokhlin dimension at most one. A consequence of these observations is a relationship between the nuclear dimension of an O\mathcal O_\infty-absorbing C*-algebra and its O2\mathcal O_2-stabilization. We also give a more direct and alternative approach to this result. Several applications of this relationship are discussed to cover a fairly large class of O\mathcal O_\infty-absorbing C*-algebras that turn out to have finite nuclear dimension.

Cite this article

Selçuk Barlak, Dominic Enders, Hiroki Matui, Gábor Szabó, Wilhelm Winter, The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras. J. Noncommut. Geom. 9 (2016), no. 4, pp. 1383–1393

DOI 10.4171/JNCG/226