Abelian operator algebras are understood. General operator algebras can be analyzed by examination of large abelian subalgebras. Renault's seminal result relates Cartan subalgebras, which are abelian and particularly nice, to algebraic structures known as groupoids. The talk will define all relevant notions and proceed to explain an extension of Renault's result to the situation where a compact abelian group acts in a convenient way on a C*-algebra. This is joint work with Jonathan Brown, Adam Fuller, and David Pitts.
A Renault-type correspondence between groupoid twists and C*-algebras acted upon by abelian groups