Characterizing groupoid C* -algebras of non-Hausdorff Étale groupoids / Ruy Exel, David R. Pitts.
Exel, Ruy, 1956- author.; Pitts, David Ryder, author.
2022
QA326
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Title
Characterizing groupoid C* -algebras of non-Hausdorff Étale groupoids / Ruy Exel, David R. Pitts.
Author
Exel, Ruy, 1956- author.
ISBN
9783031055133 (electronic bk.)
3031055136 (electronic bk.)
9783031055126
3031055128
DOI
https://doi.org/10.1007/978-3-031-05513-3
Published
Cham : Springer, [2022]
Copyright
©2022
Language
English
Description
1 online resource (viii, 158 pages).
Item Number
10.1007/978-3-031-05513-3 doi
Call Number
QA326
Dewey Decimal Classification
512/.55
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and indexes.
Access Note
Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed November 1, 2022).
Added Author
Pitts, David Ryder, author.
Series
Lecture notes in mathematics (Springer-Verlag) ; 2306.
Available in Other Form
Print version: 9783031055126
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Intro
Abstract
Contents
1 Introduction
2 Inclusions
2.1 Local Modules
2.2 Regular Ideals and the Localizing Projection
2.3 Regular Inclusions
2.4 Invariant Ideals
2.5 Extended Multiplication for Normalizers
2.6 Regularity of Maximal Ideals in Regular Inclusions
2.7 Extension of Pure States, Relative Free Points and Smooth Normalizers
2.8 Free Points
2.9 Fourier Coefficients
2.10 Opaque and Gray Ideals
2.11 Topologically Free Inclusions
2.12 Pseudo-Expectations
3 Groupoids
3.1 Étale Groupoids
3.2 Twists and Line Bundles

3.3 The C*-Algebra of a Twisted Groupoid
3.4 Topologically Free Groupoids
3.5 The Essential Groupoid C*-Algebra
3.6 Kwasniewski and Meyer's Version of the Essential Groupoid C*-Algebra
3.7 The Relative Weyl Groupoid
3.8 Fell Bundles Over Inverse Semigroups
3.9 Topological Freeness of the Weyl Groupoidand the Main Theorem
3.10 Semi-Masas
3.11 Canonical States
4 Examples and Open Questions
4.1 Example: Non-Smooth Normalizers
4.2 Example: Periodic Functions on the Interval
4.3 Example: The Gray Ideal of Twisted Groupoid C*-Algebras
4.4 Some Open Questions

5 Appendix: Isotropy Projection
References
Symbol Index
Concept Index

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