Abstract

The focus of this minicourse is the construction of C-algebras from groupoids on the one hand, andthe reconstruction of groupoids from C-algebras with Cartan subalgebras on the other hand. Guided bycommon examples, we will start with a basic introduction to topological groupoids and so-called twistsover them. In the special case of etale groupoids, we will then see how to build the associated twisted ´reduced C-algebra, and how Kumjian–Renault theory provides an inverse process: if the groupoid hasno (open) abelian subgroupoids (ie, the groupoid is “effective”), then one can reconstruct it from itsC-algebra together with a “canonical” abelian subalgebra. If time permits, we will have a look at thenon-effective situation.Futher prepartory reading (this will not be assumed) In much of the first half of this minicourse, I willbe following Part II of the book “Operator Algebras and Dynamics: Groupoids, Crossed products, andRokhlin dimension” by Sims–Szabo–Williams. The interested participant can find further information ´on groupoid C-algebras in Williams’ book “A Tool Kit for Groupoid C-Algebras.”