Analysis Seminar

Adam Fuller, Ohio University

"Describing C*-algebras in terms of topological groupoids"

Unital abelian C*-algebras are well understood. They are necessarily isomorphic to C(X), the continuous functions on a compact Hausdorff space X. Studying the topological dynamics on $X$ gives rise to the study of crossed product C*-algebras: a class of relatively well understood of non-abelian operator algebras constructed from a dynamical system.

Turning the problem on its head you can ask: if A is a C*-algebra containing an abelian C*-algebra D=C(X) to what extent does A determine dynamics on X, and when can A be recovered from this dynamics. Kumjian (1986), and then Renault (2008), showed that if D is a Cartan subalgebra of A then the groupoid structure of the dynamics A induces on X recovers A as a reduced C*-algebra of a groupoid twist. In this talk we will discuss a generalization of these results to when A is topologically graded by a discrete abelian group $\Gamma$, with D a Cartan subalgebra of A₀. This is joint work with Jon Brown, David Pitts and Sarah Reznikoff.

MC 5417