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An Invitation to Quantum Groups and Duality
EMS Textbooks in Mathematics

Thomas Timmermann (University of Münster, Germany)

An Invitation to Quantum Groups and Duality

From Hopf Algebras to Multiplicative Unitaries and Beyond

ISBN print 978-3-03719-043-2, ISBN online 978-3-03719-543-7
DOI 10.4171/043
February 2008, 427 pages, hardcover, 16.5 x 23.5 cm.
58.00 Euro

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, Baaj–Skandalis-duality, and approaches to quantum groupoids in the setting of operator algebras.

The book is addressed to graduate students and non-experts 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.

Keywords: Hopf algebras, duality, multiplicative unitaries, quantum groups, quantum groupoids

Further Information

Review in Zentralblatt MATH 05246363

Review in MR 2397671

EMS Review

MAA Review