Sven Raum: Simplicity of essential groupoid C*-algebras
Time: Wed 2021-12-08 13.15 - 14.15
Lecturer: Sven Raum (SU)
Groupoids merge the notion of space and group, yielding a well-adapted framework to study dynamical systems from an algebraic and analytic perspective. For decades, operator algebraists have studied various C*-algebras and von Neumann algebras associated to groupoids, because they provide a bridge to other areas like geometry and dynamics and describe important structural features of operator algebras themselves. In the focus of C*-algebraists, often are étale groupoids, which generalise the notion of discrete groups.
To every étale groupoid with locally compact Hausdorff space of units, one can associate an essential groupoid C*-algebra. For Hausdorff groupoids, it equals the better known reduced groupoid C*-algebra. Until recently, it had been an open problem to characterise simplicity of such essential groupoid C*-algebras. Even for Hausdorff groupoids, only partial results were known.
In this talk, I will report on joint work with Matthew Kenney, Se-Jin Kim, Xin Li and Dan Ursu, which characterises étale groupoids with locally compact Hausdorff space of units whose essential groupoid C*-algebra is simple. Our characterisation is phrased in terms of what is called essentially confined amenable sections of isotropy groups, a notion that can be checked in concrete cases. This provides a complete solution of the open problem. In particular, it comes as a surprise that non-Hausdorff groupoids fit well into this general picture. Our work extends and unifies previous results among others on C*-simplicity of discrete groups, their topological dynamical systems and groupoids of germs.
I will keep this talk accessible for an audience of non-experts, starting with a motivation and explanation of groupoids themselves, before discussing operator algebraic aspects of our work.
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