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Morita Equivalence and Continuous-Trace $C^*$-Algebras

Morita Equivalence and Continuous-Trace $C^*$-Algebras

by

Iain Raeburn and Dana P. Williams

In this text, Iain Raeburn and I give a modern treatment of the classification of continuous-trace $C^*$-algebras up to Morita equivalence. This includes a detailed discussion of Morita equivalence of $C^*$-algebras, a review of the necessary sheaf cohomology, and an introduction to recent developments in the area. The book is accessible to students who are beginning research in operator algebras after a standard one-term course in $C^*$-algebras. We have included introductions to necessary but nonstandard background. Thus we have developed the general theory of Morita equivalence using Hilbert modules, discussed the spectrum and primitive ideal space of a $C^*$-algebra including many examples, and presented the necessary facts on tensor products of $C^*$-algebras starting from scratch. Motivational material and comments designed to place the theory in a more general context are included. The text is self-contained and would be suitable for an advanced graduate or an independent study course.

• This book is volume 60 of the American Mathematical Society's Survey and Monograph series (ISBN 0-8218-0860-5), and may be purchased from the Society's online bookstore.
• An HTML version of the table of contents is available.
• We are compiling a list of typographical errors and corrections, and the most current version is available here.
• We would appreciate seeing any comments you have and/or typographical errors you might find. You can email either of us at dana DOT williams AT dartmouth DOT edu or iraeburn AT maths DOT otago DOT ac DOT au.

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Last modified on December 21, 2012