Fundamentals of Hopf Algebras
This text aims to provide graduate students with a self-contained introduction to topics that are at the forefront of modern algebra, namely, coalgebras, bialgebras, and Hopf algebras. The last chapter (Chapter 4) discusses several applications of H
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Robert G. Underwood
Fundamentals of Hopf Algebras
Universitext
Universitext Series Editors Sheldon Axler San Francisco State University Vincenzo Capasso Università degli Studi di Milano Carles Casacuberta Universitat de Barcelona Angus MacIntyre Queen Mary University of London Kenneth Ribet University of California, Berkeley Claude Sabbah CNRS, École polytechnique, Paris Endre Süli University of Oxford Wojbor A. Woyczynski Case Western Reserve University, Cleveland, OH
Universitext is a series of textbooks that presents material from a wide variety of mathematical disciplines at master’s level and beyond. The books, often well class-tested by their author, may have an informal, personal even experimental approach to their subject matter. Some of the most successful and established books in the series have evolved through several editions, always following the evolution of teaching curricula, to very polished texts. Thus as research topics trickle down into graduate-level teaching, first textbooks written for new, cutting-edge courses may make their way into Universitext.
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Robert G. Underwood
Fundamentals of Hopf Algebras
123
Robert G. Underwood Department of Mathematics and Computer Science Auburn University at Montgomery Montgomery, AL, USA
ISSN 0172-5939 ISSN 2191-6675 (electronic) Universitext ISBN 978-3-319-18990-1 ISBN 978-3-319-18991-8 (eBook) DOI 10.1007/978-3-319-18991-8 Library of Congress Control Number: 2015939602 Mathematics Subject Classification (2010): 11Axx, 12E20, 13Axx, 16T05, 16T10, 16T15 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 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 omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www. springer.com)
to my mother and father
Preface
The purpose of this text is to provide an introduction to the
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