Mathias Palmstrøm: Exotic C*-completions of étale groupoids

Abstract: An exotic groupoid C*-algebra associated to an étale groupoid G is a completion of the convolution algebra C_c(G) in a C*-norm that dominates the reduced norm and differs from both the reduced and full. For locally compact groups, the problem of finding exotic group C*-algebras has attracted a lot of attention over the last decade. One fruitful way of obtaining these has been to consider ideal completions as introduced by Brown and Guentner. For certain groups, many such C*-completions have been shown to be exotic group C*-algebras. In this talk, I will explain how the construction of Brown and Guentner can be generalized to second countable Hausdorff étale groupoids, and using this construction, provide examples of exotic groupoid C*-algebras associated to hyperbolic groupoids and double groupoids.