EMS Textbooks in Mathematics 2008; 427 pp; hardcover Volume: 5 ISBN10: 3037190434 ISBN13: 9783037190432 List Price: US$78 Member Price: US$62.40 Order Code: EMSTEXT/5
 This book provides an introduction to the theory of quantum groups with emphasis on their duality and on the setting of operator algebras. Part I of the text presents the basic theory of Hopf algebras, Van Daele's duality theory of algebraic quantum groups, and Woronowicz's compact quantum groups, staying in a purely algebraic setting. Part II focuses on quantum groups in the setting of operator algebras. Woronowicz's compact quantum groups are treated in the setting of \(C^*\)algebras, and the fundamental multiplicative unitaries of Baaj and Skandalis are studied in detail. An outline of Kustermans' and Vaes' comprehensive theory of locally compact quantum groups completes this part. Part III leads to selected topics, such as coactions, BaajSkandalisduality, and approaches to quantum groupoids in the setting of operator algebras. The book is addressed to graduate students and nonexperts from other fields. Only basic knowledge of (multi) linear algebra is required for the first part, while the second and third part assume some familiarity with Hilbert spaces, \(C^*\)algebras, and von Neumann algebras. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in quantum groups. Table of Contents Part I. From groups to quantum groups  Hopf algebras
 Multiplier Hopf algebras and their duality
 Algebraic compact quantum groups
Part II. Quantum groups and \(C^*\)/von Neumann bialgebras  First definitions and examples
 \(C^*\)algebraic compact quantum groups
 Examples of compact quantum groups
 Multiplicative unitaries
 Locally compact quantum groups
Part III. Selected topics  Coactions on \(C^*\)algebras, reduced crossed products, and duality
 Pseudomultiplicative unitaries on Hilbert spaces
 Pseudomultiplicative unitaries on \(C^*\)modules
 Appendix
 Bibliography
 Symbol Index
 Index
