Morita Equivalence and Continuous-Trace $C^*$-Algebras
About this Title
Iain Raeburn, University of Newcastle, NSW, Australia and Dana P. Williams, Dartmouth College, Hanover, NH
Publication: Mathematical Surveys and Monographs
Publication Year: 1998; Volume 60
ISBNs: 978-0-8218-0860-3 (print); 978-1-4704-1287-6 (online)
MathSciNet review: MR1634408
MSC: Primary 46L05; Secondary 22D99, 46L55, 46M20
In this text, the authors 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. The authors have included introductions to necessary but nonstandard background. Thus they have developed the general theory of Morita equivalence from the Hilbert module, 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.
Graduate students, research mathematicians, and mathematical physicists working in operator algebras, Morita equivalence, or continuous-trace $C^*$-algebras.
Table of Contents
- 1. The algebra of compact operators
- 2. Hilbert $C$*-modules
- 3. Morita equivalence
- 4. Sheaves, cohomology, and bundles
- 5. Continuous-trace $C$*-algebras
- 6. Applications
- 7. Epilogue: The Brauer group and group actions