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Crossed Products of \(C^*\)-Algebras
Dana P. Williams, Dartmouth College, Hanover, NH
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Mathematical Surveys and Monographs
2007; 528 pp; hardcover
Volume: 134
ISBN-10: 0-8218-4242-0
ISBN-13: 978-0-8218-4242-3
List Price: US$112
Member Price: US$89.60
Order Code: SURV/134
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The theory of crossed products is extremely rich and intriguing. There are applications not only to operator algebras, but to subjects as varied as noncommutative geometry and mathematical physics. This book provides a detailed introduction to this vast subject suitable for graduate students and others whose research has contact with crossed product \(C^*\)-algebras. In addition to providing the basic definitions and results, the main focus of this book is the fine ideal structure of crossed products as revealed by the study of induced representations via the Green-Mackey-Rieffel machine. In particular, there is an in-depth analysis of the imprimitivity theorems on which Rieffel's theory of induced representations and Morita equivalence of \(C^*\)-algebras are based. There is also a detailed treatment of the generalized Effros-Hahn conjecture and its proof due to Gootman, Rosenberg, and Sauvageot.

This book is meant to be self-contained and accessible to any graduate student coming out of a first course on operator algebras. There are appendices that deal with ancillary subjects, which while not central to the subject, are nevertheless crucial for a complete understanding of the material. Some of the appendices will be of independent interest.

To view another book by this author, please visit Morita Equivalence and Continuous-Trace \(C^*\)-Algebras.

Readership

Graduate students and research mathematicians interested in \(C^*\)-algebras.

Reviews

"The aim of this nicely written and self-contained book is to provide the tools necessary to begin doing research involving crossed product \(C^*\)-algebras."

-- Zentralblatt MATH

"This is the first book devoted exclusively to the theory of \(C^*\)-crossed products, and will be especially useful to graduate students trying to learn something about them. ... A valuable extra feature of this book is the extensive set of appendices (about 200 pages worth!), covering a number of topics of independent interest, such as amenability, Borel structures, direct integrals, and the Fell topology on representations and ideals."

-- Jonathan M. Rosenberg for Mathematical Reviews

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