Construction of minimal skew products of amenable minimal dynamical systems

Abstract

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.

15 pages, Final version. To appear in Groups, Geometry, and Dynamics

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