Groups, Geometry, and Dynamics


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Volume 11, Issue 1, 2017, pp. 75–94
DOI: 10.4171/GGD/388

Published online: 2017-04-20

Construction of minimal skew products of amenable minimal dynamical systems

Yuhei Suzuki[1]

(1) University of Tokyo, Japan

For an amenable minimal topologically free dynamical system $\alpha$ of a group on a compact metrizable space $Z$ and for a compact metrizable space $Y$ satisfying a mild condition, we construct a minimal skew product extension of $\alpha$ on $Z \times Y$. This generalizes a result of Glasner and Weiss. We also study the pure infiniteness of the crossed products of minimal dynamical systems arising from this result. In particular, we give a generalization of a result of Rørdam and Sierakowski.

Keywords: $C^*$-algebras, amenable actions, pure infiniteness

Suzuki Yuhei: Construction of minimal skew products of amenable minimal dynamical systems. Groups Geom. Dyn. 11 (2017), 75-94. doi: 10.4171/GGD/388