Approaching the UCT problem via crossed products of the Razak–Jacelon algebra

  • Selçuk Barlak

    Europa-Universität Flensburg, Germany
  • Gábor Szabó

    University of Leuven, Belgium
Approaching the UCT problem via crossed products of the Razak–Jacelon algebra cover

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Abstract

We show that the UCT problem for separable, nuclear 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 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 C*-algebras, as well as a known characterization of the UCT problem in terms of certain tracially AF C*-algebras due to Dadarlat.

Cite this article

Selçuk Barlak, Gábor Szabó, Approaching the UCT problem via crossed products of the Razak–Jacelon algebra. Groups Geom. Dyn. 14 (2020), no. 1, pp. 137–149

DOI 10.4171/GGD/538