Hardcover ISBN:  9781470451332 
Product Code:  SURV/241 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
Electronic ISBN:  9781470454098 
Product Code:  SURV/241.E 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 

Book DetailsMathematical Surveys and MonographsVolume: 241; 2019; 398 ppMSC: 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 BaumConnes 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 selfcontained and accessible to graduate students with a good background in operator algebras.ReadershipGraduate students and researchers interested in \(C^{*}\)algebras.

Table of Contents

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

Comments on simplicity

Duals and topological vector spaces

Remarks on Blanchard’s Theorem

The inductive limit topology

Ramsay almost everywhere

Answers to some of the exercises


Additional Material

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, HeriotWatt University 
This graduatelevel 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


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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 BaumConnes 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 selfcontained 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

Comments on simplicity

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, HeriotWatt University 
This graduatelevel 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