Quantum Groups and Noncommutative Geometry
This textbook presents the second edition of Manin's celebrated 1988 Montreal lectures, which influenced a new generation of researchers in algebra to take up the study of Hopf algebras and quantum groups. In this expanded write-up of those lectures, Mani
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Yuri I. Manin
Quantum Groups and Noncommutative Geometry Second Edition With a Contribution by Theo Raedschelders and Michel Van den Bergh
CRM Short Courses Series Editors Galia Dafni, Concordia University, Montreal, QC, Canada Véronique Hussin, University of Montreal, Montreal, QC, Canada
Editorial Board Mireille Bousquet-Mélou (CNRS, LaBRI, Université de Bordeaux) Antonio Córdoba Barba (ICMAT, Universidad Autónoma de Madrid) Svetlana Jitomirskaya (UC Irvine) V. Kumar Murty (University of Toronto) Leonid Polterovich (Tel-Aviv University)
The volumes in the CRM Short Courses series have a primarily instructional aim, focusing on presenting topics of current interest to readers ranging from graduate students to experienced researchers in the mathematical sciences. Each text is aimed at bringing the reader to the forefront of research in a particular area or field, and can consist of one or several courses with a unified theme. The inclusion of exercises, while welcome, is not strictly required. Publications are largely but not exclusively, based on schools, instructional workshops and lecture series hosted by, or affiliated with, the Centre de Researches Mathématiques (CRM). Special emphasis is given to the quality of exposition and pedagogical value of each text.
More information about this series at http://www.springer.com/series/15360
Yuri I. Manin
Quantum Groups and Noncommutative Geometry Second Edition With a Contribution by Theo Raedschelders and Michel Van den Bergh
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Yuri I. Manin Max Planck Institute for Mathematics Bonn, Germany
ISSN 2522-5200 ISSN 2522-5219 (electronic) CRM Short Courses ISBN 978-3-319-97986-1 ISBN 978-3-319-97987-8 (eBook) https://doi.org/10.1007/978-3-319-97987-8 Library of Congress Control Number: 2018950779 Mathematics Subject Classification (2010): 16S10, 16S37, 16S38, 16T05, 16T15, 16W30, 18D50, 18D10, 20C30, 20G42 1st edition: © Centre de Recherches Mathématiques 1988 2nd edition: © Springer Nature Switzerland AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or
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