Characterizing Groupoid C*-algebras of Non-Hausdorff Étale Groupoids (Lecture Notes in Mathematics)

Exel, Ruy/ Pitts, David R.

Springer International Publishing AG（2022/10発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 158 p.
• 商品コード 9783031055126

Full Description

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.

Contents

- 1. Introduction. - 2. Inclusions. - 3. Groupoids. - 4. Examples and Open Questions. - 5. Appendix.