Characterizing Groupoid C*-algebras of Non-Hausdorff Étale Groupoids (Lecture Notes in Mathematics, 2306)
Springer
ISBN13:
9783031055126
$56.30
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 KumjianRenault 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 KumjianRenault theory to a 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.
- | Author: Ruy Exel, David Pitts
- | Publisher: Springer
- | Publication Date: Oct 20, 2022
- | Number of Pages: 166 pages
- | Language: English
- | Binding: Paperback/Mathematics
- | ISBN-10: 3031055128
- | ISBN-13: 9783031055126
- Author:
- Ruy Exel, David Pitts
- Publisher:
- Springer
- Publication Date:
- Oct 20, 2022
- Number of pages:
- 166 pages
- Language:
- English
- Binding:
- Paperback/Mathematics
- ISBN-10:
- 3031055128
- ISBN-13:
- 9783031055126