The Primitive Ideals of some Étale Groupoid C ∗-Algebras

Abstract

We consider the Deaconu–Renault groupoid of an action of a finitely generated free abelian monoid by local homeomorphisms of a locally compact Hausdorff space. We catalogue the primitive ideals of the associated groupoid C ∗-algebra. For a special class of actions we describe the Jacobson topology.