Title: A canonical Cartan subalgebra for the C*-algebra of an etale groupoid
Speaker: Jonathan Brown (University of Dayton)
Abstract: In a 2008 paper, Renault studied a special class of maximal abelian subalgebras of a C*-algebra which he called Cartan. He showed that if G is a groupoid, the continuous functions on the unit space includes into the reduced C*-algebra of the groupoid is Cartan if G is topologically principal. If G is not topologically principal, then the algebra of continuous functions on the unit space is not maximal abelian. In this talk we consider a larger subalgebra M of the reduced groupoid C*-algebra which can be constructed using the interior of the isotropy of G. We characterize exactly when M is Cartan using properties of G and show that the set of pure states on M with unique extension to the reduced groupoid C*-algebra is dense and deduce a Cuntz-Krieger type uniqueness theorem. This talk will be on two papers, one is joint with G. Nagy, S. Reznikoff, A. Sims and D. Williams and the other is joint with H. Li and D. Yang.