Representations of Groupoid C*-algebras and Fredholm Groupoids

Yu Qiao 乔雨  (Shaanxi Normal University)

15:30-16:30, June 8, 2018   Science Building A504

Abstract:

In the 1980s, Alain Connes initiated his program of noncommutative differential geometry, especially the study of “bad” spaces. It turns out that (Lie) groupoids are an effective tool to model many analysis and index problems on singular spaces. In this talk, we first review the construction of group C*-algebras via the representation theory of groups, the notion of Lie groupoids, and the construction of groupoid C ∗ -algebras via the representation theory of C ∗ -algebras. Then we give the concept of a Fredholm groupoid, in some sense, the largest class of groupoids for which certain Fredholm criteria hold with respect to a natural class of representations, namely the regular representations of a groupoid. Finally we investigate the relations among Fredholm groupids and some families of representations of groupoid C*-algebras. This is joint work with Catarina Carvalho and Victor Nistor.

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