Ruy Exel (Universidade Federal de Santa Catarina)

Wednesday 12th April, 2023 16:00-17:00 Maths 311B


In 2008, building on earlier work of Feldman, Moore and Kumjian, Jean Renault introduced the notion of Cartan inclusions of C*-algebras and proved that these correspond bijectively to twisted, essentially principal, Hausdorff  etale groupoids via the reduced groupoid C*-algebra construction.

Since non-Hausdorff groupoids are also knownn to lead to important examples of inclusions of C*- algebras, a natural question is to try to characterize the inclusions of C*-algebras arising from non-Hausdorff groupoids. The goal of this talk is to describe a set of results developped by David Pitts and myself, and published in a recent Springer Lecture Notes, deriving such a characterization. Along the way I will also attempt to describe a result that gives a characterization of C*-algebras of twisted, Hausdorff,  etale groupoids without the assumption that the groupoid be essentially principal. Among other things, this result applies to the very prosaic inclusion C(S^1)  in C[0,2\pi], obtained by thinking of functions on the circle as 2-periodic functions, which is therefore shown to be modeled by a twisted groupoid. Can you guess which?

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