A Tool Kit for Groupoid $C^{*}$-Algebras
Seiten
2019
American Mathematical Society (Verlag)
978-1-4704-5133-2 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-5133-2 (ISBN)
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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.
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.
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.
Dana P. Williams, Dartmouth College, Hanover, NH.
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
Notation and symbol index
Index
Bibliography.
Erscheinungsdatum | 16.08.2019 |
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Reihe/Serie | Mathematical Surveys and Monographs |
Verlagsort | Providence |
Sprache | englisch |
Maße | 178 x 254 mm |
Gewicht | 925 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Analysis | |
ISBN-10 | 1-4704-5133-6 / 1470451336 |
ISBN-13 | 978-1-4704-5133-2 / 9781470451332 |
Zustand | Neuware |
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