Construction of minimal skew products of amenable minimal dynamical systems

TL;DR

This paper constructs minimal skew product extensions of amenable minimal dynamical systems on compact spaces and investigates the pure infiniteness of their crossed products, generalizing previous results by Glasner-Weiss and Rordam-Sierakowski.

Contribution

It introduces a method to build minimal skew products for amenable minimal systems and analyzes the pure infiniteness of their crossed products, extending prior work in the field.

Findings

Successfully constructed minimal skew products for a broad class of systems.

Established conditions under which the crossed products are purely infinite.

Generalized key results on pure infiniteness from Rordam and Sierakowski.

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 R{\o}rdam and Sierakowski.