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

Name: Characterizing Groupoid C*-algebras of Non-Hausdorff Étale Groupoids
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ISBN: 9783031055126

Ruy Exel, David R. Pitts

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English

Springer International Publishing AG
20 October 2022

Groups & group theory; Functional analysis & transforms

Series: Lecture Notes in Mathematics

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.

By: Ruy Exel, David R. Pitts
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2022
Volume: 2306
Dimensions: Height: 235mm, Width: 155mm,
Weight: 267g
ISBN: 9783031055126
ISBN 10: 3031055128
Series: Lecture Notes in Mathematics
Pages: 158
Publication Date: 20 October 2022
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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

Ruy Exel is a professor of Mathematics at the Universidade Federal de Santa Catarina, in Brazil. He has published extensively in the subject of operator algebras with emphasis on its interactions with dynamical systems and mathematical physics. A pioneer in the area of partial actions of groups on C*-algebras, he has recently published the book Partial Dynamical Systems, Fell Bundles and Applications. He was an invited speaker in the 2018 ICM in Rio. David R. Pitts is a professor of mathematics at the University of Nebraska–Lincoln. He has published work on various aspects of operator algebras, including: commutative subspace lattice algebras, free semigroup algebras, and Cartan subalgebras of von Neumann algebras and C*-algebras.

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

“This is a nicely written monograph devoted to the new and important notion of non Hausdorff groupoids and their C*-algebras, and could be beneficial for researchers in operator algebras and mathematical physics.” (Massoud Amini, zbMATH 1511.46002, 2023)