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A Tool Kit for Groupoid $C^{*}$-Algebras

Dana P. Williams Dartmouth College, Hanover, NH
Available Formats:
Hardcover ISBN: 978-1-4704-5133-2
Product Code: SURV/241
List Price: $129.00 MAA Member Price:$116.10
AMS Member Price: $103.20 Electronic ISBN: 978-1-4704-5409-8 Product Code: SURV/241.E List Price:$129.00
MAA Member Price: $116.10 AMS Member Price:$103.20
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List Price: $193.50 MAA Member Price:$174.15
AMS Member Price: $154.80 Click above image for expanded view A Tool Kit for Groupoid$C^{*}$-Algebras Dana P. Williams Dartmouth College, Hanover, NH Available Formats:  Hardcover ISBN: 978-1-4704-5133-2 Product Code: SURV/241  List Price:$129.00 MAA Member Price: $116.10 AMS Member Price:$103.20
 Electronic ISBN: 978-1-4704-5409-8 Product Code: SURV/241.E
 List Price: $129.00 MAA Member Price:$116.10 AMS Member Price: $103.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$193.50 MAA Member Price: $174.15 AMS Member Price:$154.80
• Book Details

Mathematical Surveys and Monographs
Volume: 2412019; 398 pp
MSC: Primary 46; Secondary 22;

The construction of a $C^{*}$-algebra from a locally compact groupoid is an important generalization of the group $C^{*}$-algebra construction and of the transformation group $C^{*}$-algebra construction. Since their introduction in 1980, groupoid $C^{*}$-algebras have been intensively studied with diverse applications, including graph algebras, classification theory, variations on the Baum-Connes conjecture, and noncommutative geometry. This book provides a detailed introduction to this vast subject and is suitable for graduate students or any researcher who wants to use groupoid $C^{*}$-algebras in their work. The main focus is to equip the reader with modern versions of the basic technical tools used in the subject, which will allow the reader to understand fundamental results and make contributions to various areas in the subject. Thus, in addition to covering the basic properties and construction of groupoid $C^{*}$-algebras, the focus is to give a modern treatment of some of the major developments in the subject in recent years, including the Equivalence Theorem and the Disintegration Theorem. Also covered are the complicated subjects of amenability of groupoids and simplicity results.

The book is reasonably self-contained and accessible to graduate students with a good background in operator algebras.

Graduate students and researchers interested in $C^{*}$-algebras.

• Chapters
• From groupoid to algebra
• Groupoid actions and equivalence
• Measure theory
• Proof of the Equivalence Theorem
• Basic representation theory
• The existence and uniqueness of Haar systems
• Unitary representations
• Renault’s Disintegration Theorem
• Amenability for groupoids
• Measurewise amenability for groupoids
• Duals and topological vector spaces
• Remarks on Blanchard’s Theorem
• The inductive limit topology
• Ramsay almost everywhere
• Answers to some of the exercises

• Reviews

• The book is written as a textbook with exercises at the end of each chapter, which is ideal for experts, but for the rest of us, this is a superb reference for particular topics that are currently only to be found scattered throughout the literature.

Mark V. Lawson, Heriot-Watt University
• This graduate-level textbook is a comprehensive, readable introduction to the fundamental theory of groupoid C*-algebras. No textbook can make groupoid C*-theory easy, but A Tool Kit for Groupoid C*-Algebras finally makes it accessible.

Elizabeth Gillaspy, University of Montana
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 2412019; 398 pp
MSC: Primary 46; Secondary 22;

The construction of a $C^{*}$-algebra from a locally compact groupoid is an important generalization of the group $C^{*}$-algebra construction and of the transformation group $C^{*}$-algebra construction. Since their introduction in 1980, groupoid $C^{*}$-algebras have been intensively studied with diverse applications, including graph algebras, classification theory, variations on the Baum-Connes conjecture, and noncommutative geometry. This book provides a detailed introduction to this vast subject and is suitable for graduate students or any researcher who wants to use groupoid $C^{*}$-algebras in their work. The main focus is to equip the reader with modern versions of the basic technical tools used in the subject, which will allow the reader to understand fundamental results and make contributions to various areas in the subject. Thus, in addition to covering the basic properties and construction of groupoid $C^{*}$-algebras, the focus is to give a modern treatment of some of the major developments in the subject in recent years, including the Equivalence Theorem and the Disintegration Theorem. Also covered are the complicated subjects of amenability of groupoids and simplicity results.

The book is reasonably self-contained and accessible to graduate students with a good background in operator algebras.

Graduate students and researchers interested in $C^{*}$-algebras.

• Chapters
• From groupoid to algebra
• Groupoid actions and equivalence
• Measure theory
• Proof of the Equivalence Theorem
• Basic representation theory
• The existence and uniqueness of Haar systems
• Unitary representations
• Renault’s Disintegration Theorem
• Amenability for groupoids
• Measurewise amenability for groupoids
• Duals and topological vector spaces
• Remarks on Blanchard’s Theorem
• The inductive limit topology
• Ramsay almost everywhere
• Answers to some of the exercises
• The book is written as a textbook with exercises at the end of each chapter, which is ideal for experts, but for the rest of us, this is a superb reference for particular topics that are currently only to be found scattered throughout the literature.

Mark V. Lawson, Heriot-Watt University
• This graduate-level textbook is a comprehensive, readable introduction to the fundamental theory of groupoid C*-algebras. No textbook can make groupoid C*-theory easy, but A Tool Kit for Groupoid C*-Algebras finally makes it accessible.

Elizabeth Gillaspy, University of Montana
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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