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Journal of Noncommutative Geometry


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Volume 9, Issue 4, 2015, pp. 1383–1393
DOI: 10.4171/JNCG/226

Published online: 2016-01-06

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

Selçuk Barlak[1], Dominic Enders[2], Hiroki Matui[3], Gábor Szabó[4] and Wilhelm Winter[5]

(1) University of Southern Denmark, Odense, Denmark
(2) University of Copenhagen, Denmark
(3) Chiba University, Japan
(4) Westfälische Wilhelms-Universität Münster, Germany
(5) Westfälische Wilhelms-Universität Münster, Germany

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 $\mathcal O_\infty$-absorbing C*-algebra and its $\mathcal O_2$-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 $\mathcal O_\infty$-absorbing C*-algebras that turn out to have finite nuclear dimension.

Keywords: Kirchberg algebra, nuclear dimension, Rokhlin dimension

Barlak Selçuk, Enders Dominic, Matui Hiroki, Szabó Gábor, Winter Wilhelm: The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras. J. Noncommut. Geom. 9 (2015), 1383-1393. doi: 10.4171/JNCG/226