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.