Cartan subalgebras for non-principal twisted groupoid C*-algebras

Anna Duwenig  (University of Wollongong, Australia)

15:00-16:00, April 15, 2022   Zoom Meeting ID: 813 6886 3279 (Passcode: 519643)

Abstract:

The reduced C*-algebra of a topologically principal twisted groupoid has a canonical Cartan subalgebra: functions on its unit space. A remarkable Weyl groupoid construction, due to Kumjian and Renault, asserts the converse: If a C*-algebra A admits a Cartan subalgebra, there exists such a groupoid whose C*-algebra is isomorphic to A in a Cartan-preserving way. In this talk, I will present on joint work with Gillaspy, Norton, Reznikoff, and Wright, in which we identified subgroupoids of (not necessarily topologically principal) groupoids that give rise to Cartan subalgebras. If time permits, I will further give an explicit description of the associated Weyl groupoid and twist, which is based on further joint work with Gillaspy and Norton.