The primitive ideal space of Deaconu–Renault groupoid C*-algebras

Abstract

The main goal of this thesis is to reproduce the article [SW16] by Sims and Williams, categorising the primitive ideal space of the class of Deaconu- Renault groupoid C*-algebras generated by N_0^k-actions. We go through the required groupoid prerequisites, from the definition of a groupoid to the construction of covariance C*-algebras. We apply what we learn from [SW16] to study simplicity of the covariance C*-algebras, and give an explicit application to the rotation algebra.