Noncommutative Geometry and Topology in Prague

C*-irreducible regular inclusions

Recently there has been a lot of research on C*-inclusions with the property that every intermediate C*-algebra is simple. Last  year, Mikael Rørdam initiated a systematic study of such inclusions, which he called C*-irreducible.  I will use this notion as an excuse to present some of the results of my recent work with Ralph Meyer. I will discuss the relationship between C*-irreducibility, aperiodicity, the almost extension property and noncommutative Cartan inclusions in the sense of Ruy Exel. This leads to a characterisation of regular C*-irreducible inclusions by a long list of equivalent conditions, one being that the inclusion comes from an outer Fell bundle over a discrete group.