Characterizing groupoid C*-algebras of non-Hausdorff étale groupoids
著者
書誌事項
Characterizing groupoid C*-algebras of non-Hausdorff étale groupoids
（Lecture notes in mathematics, v. 2306）
Springer, c2022
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注記
Includes bibliographical references (p. 151-152) and indexes
内容説明・目次
内容説明
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 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.
目次
- 1. Introduction. - 2. Inclusions. - 3. Groupoids. - 4. Examples and Open Questions. - 5. Appendix.
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