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Thomas Timmermann (University of Münster, Germany)
An Invitation to Quantum Groups and Duality
From Hopf Algebras to Multiplicative Unitaries and BeyondISBN 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
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