UK Virtual OA Seminar: Groupoids for C*-algebras

Karen Strung (Czech Academy of Sciences)

Thursday 16th July, 2020 16:00-16:45 Contact Mike Whittaker for Zoom info


Groupoids are a generalisation of groups where multiplication is only partially defined. When equipped with a so-called “étale” topology, they can be considered as generalisations of discrete groups. In his thesis, Jean Renault initiated the study of the C*-algebras of groupoids. The construction of a C*-algebra from an étale groupoid generalizes not only the construction of a discrete group C*-algebra, but also many well-known constructions such as crossed products of commutative C*-algebras, Cuntz--Krieger C*-algebras, as well as other constructions related to dynamical systems such as C*-algebras from Smale spaces and tiling C*-algebras. I will discuss the basics of étale groupoid C*-algebras as well as the role that groupoids have played—and continue to play—as models for various classes of C*-algebras, particularly those related to the classification programme—those that are separable, simple, nuclear and Jiang-Su stable.

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