Johannes Christensen: Ideal structure of étale groupoid C*-algebras

Abstract: There are many different constructions which one can use to build C*-algebras from some kind of initial data. To name a few examples one can construct C*-algebras from discrete groups, directed graphs, group actions by homeomorphisms and many other kinds of dynamical systems. The C*-algebras constructed from such data might not be simple, in which case it is interesting to understand the ideal structure of the C*-algebra.
 
The primitive spectrum of a C*-algebra consists of the ideals that can be realized as kernels of irreducible representations. When equipped with the Jacobson topology, this space completely determines the ideal structure of the C*-algebra. It has however often proven difficult to give a complete description of the Jacobson topology.
 
There is a general framework for constructing C*-algebras using étale groupoids which generalises all the aforementioned constructions. In this talk I will report on a joint project with Sergey Neshveyev where we describe the primitive ideal space and its Jacobsen topology for a large class of étale groupoid C*-algebras.