Title: Building C*-Algebras from Lie Groupoids: What do we gain?
Abstract: Operator algebras and geometry have been shown to work hand in hand as pioneered by Alain Connes. In the "big book", Alain Connes makes the case that groupoids are a necessary object to consider and study for geometric and operator algebras research. In operator algebras, many well known C*-algebras actually arise as groupoid C*-algebras, allowing us to apply groupoid techniques to these C*-algebras. In geometry, groupoids are built and arise from bundles and foliations. In this talk, I will define general and Lie groupoids. Then give a basic overview of how to build the reduced and full groupoid C*-algebras from a locally compact Hausdorff groupoid with a Haar system and then contrast that construction with the "natural" construction you can perform to build the reduced and full groupoid C*-algebras from a Lie groupoid. After doing this and discussing what we gain from this so called "natural" construction, we will see that we do in fact obtain the same C*-algebras regardless of using a Haar system or this "natural" construction.
