An Invitation To Quantum Groups And Duality (ems Textbooks In Mathematics)

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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.

E-Book Content

Timmermann_titelei 31.1.2008 16:36 Uhr Seite 1 M M S E M E S E S E M E S M S Timmermann_titelei 31.1.2008 16:36 Uhr Seite 2 EMS Textbooks in Mathematics EMS Textbooks in Mathematics is a book series aimed at students or professional mathematicians seeking an introduction into a particular field. The individual volumes are intended to provide not only relevant techniques, results and their applications, but afford insight into the motivations and ideas behind the theory. Suitably designed exercises help to master the subject and prepare the reader for the study of more advanced and specialized literature. Jørn Justesen and Tom Høholdt, A Course In Error-Correcting Codes Markus Stroppel, Locally Compact Groups Peter Kunkel and Volker Mehrmann, Differential-Algebraic Equations Dorothee D. Haroske and Hans Triebel, Distributions, Sobolev Spaces, Elliptic Equations Timmermann_titelei 31.1.2008 16:36 Uhr Seite 3 Thomas Timmermann An Invitation to Quantum Groups and Duality From Hopf Algebras to Multiplicative Unitaries and Beyond M M S E M E S S E M E S European Mathematical Society Timmermann_titelei 31.1.2008 16:36 Uhr Seite 4 Author: Thomas Timmermann Fachbereich Mathematik und Informatik Westfälische Wilhelms-Universität Münster Einsteinstraße 62 48149 Münster Germany E-Mail: [email protected] 2000 Mathematical Subject Classification (primary; secondary): 16W30, 46-01, 46L55; 22A22, 22D25, 22D35, 46L10 Key words: Hopf algebras, duality, multiplicative unitaries, quantum groups, quantum groupoids The Swiss National Library lists this publication in The Swiss Book, the Swiss national bibliography, and the detailed bibliographic data are available on the Internet at http://www.helveticat.ch. ISBN 978-3-03719-043-2 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2008 European Mathematical Society Contact address: European Mathematical Society Publishing House Seminar for Applied Mathematics ETH-Zentrum FLI C4 CH-8092 Zürich Switzerland Phone: +41 (0)44 632 34 36 Email:
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