Properties of Topological Dynamical Systems and Corresponding $C^*$-Algebras
Properties of Topological Dynamical Systems and Corresponding $C^*$-Algebras
We show the equivalence of a certain property of topological dynamical systems $\Sigma=(X,G)$ and a particular structure of ideals in the corresponding crossed product $A(\Sigma)=C(X)\underset{\alpha}{\rtimes}G$ where $X$ is a compact set and $G$ is a discrete group. As an application, we give a complete characterization for $A(\Sigma)$ to be simple.