Crossed products of C*-algebras
著者
書誌事項
Crossed products of C*-algebras
（Mathematical surveys and monographs, v. 134）
American Mathematical Society, c2007
- : hardcover
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注記
Includes bibliographical references (p. 521-528) and index
内容説明・目次
内容説明
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.
目次
Locally compact groups Dynamical systems and crossed products Special cases and basic constructions Imprimitivity theorems Induced representations and induced ideals Orbits and quasi-orbits Properties of crossed products Ideal structure The proof of the Gootman-Rosenberg-Sauvageot theorem Amenable groups The Banach *-algebra $L^1(G,A)$ Bundles of $C*$-algebras Groups Representations of $C*$-algebras Direct integrals Effros's ideal center decomposition The Fell topology Miscellany Notation and Symbol Index Index Bibliography.
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