Characterizing Groupoid C*-algebras of Non-Hausdorff Étale Groupoids

By David R. Pitts and Ruy Exel

This book develops tools to handle C*-algebras arising as completions of convolution algebras of sections of line bundles over possibly non-Hausdorff groupoids. A fundamental result of Gelfand describes commutative C*-algebras as continuous functions on locally compact Hausdorff spaces.

Kumjian, and later Renault, showed that Gelfand's result can be extended to include non-commutative C*-algebras containing a commutative C*-algebra. In their setting, the C*-algebras in question may be described as the completion of convolution algebras of functions on twisted Hausdorff groupoids with respect to a certain norm. However, there are many natural settings in which the Kumjian-Renault theory does not apply, in part because the groupoids which arise are not Hausdorff. In fact, non-Hausdorff groupoids have been a source of surprising counterexamples and technical difficulties for decades. Including numerous illustrative examples, this book extends the Kumjian-Renault theory toa much broader class of C*-algebras.

This work will be of interest to researchers and graduate students in the area of groupoid C*-algebras, the interface between dynamical systems and C*-algebras, and related fields.

• Format: Paperback
• Language: English
• ISBN: 3031055128
• ISBN13: 9783031055126
• Release Date: October 2022
• Publisher: Springer
• Length: 158 Pages
• Weight: 0.54 lbs.
• Dimensions: 0.4" x 6.1" x 9.2"