Hopf Algebras and Their Generalizations from a Category Theoretical Point of View
These lecture notes provide a self-contained introduction to a wide range of generalizations of Hopf algebras. Multiplication of their modules is described by replacing the category of vector spaces with more general monoidal categories, thereby extending
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Gabriella Böhm
Hopf Algebras and Their Generalizations from a Category Theoretical Point of View
Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Princeton Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Gabriella B¨ohm
Hopf Algebras and Their Generalizations from a Category Theoretical Point of View
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Gabriella B¨ohm Wigner Research Centre for Physics Budapest, Hungary
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-319-98136-9 ISBN 978-3-319-98137-6 (eBook) https://doi.org/10.1007/978-3-319-98137-6 Library of Congress Control Number: 2018951456 Mathematics Subject Classification (2010): 16T10, 16T05, 18C15, 18D10, 18D15 © 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 omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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Preface
These lecture notes were originally written for a short course delivered in March 2017 at the Atlantic Algebra Centre of the Memorial University of Newfoundland, Canada. It aimed to introduce to the audience—who had some familiarity with Hopf algebra theory—a category theoretical approach to the subject. Following this recent trend, Hopf algebras, as well as a wide variety of their generalizations, are regarded as opmonoidal monads on suitable monoidal categories. A main advantage of this unified treatment is a clear conceptual explanation of the behaviour of their modules. It is a pleasure to thank the direc
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