On Characters of Finite Groups
This book explores the classical and beautiful character theory of finite groups. It does it by using some rudiments of the language of categories. Originally emerging from two courses offered at Peking University (PKU), primarily for third-year students,
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Michel Broué
On Characters of Finite Groups
Mathematical Lectures from Peking University Editor-in-chief Gang Tian, Princeton, NJ, USA
More information about this series at http://www.springer.com/series/11574
Michel Broué
On Characters of Finite Groups
123
Michel Broué Université Paris Diderot Paris 7 Paris France
ISSN 2197-4209 ISSN 2197-4217 (electronic) Mathematical Lectures from Peking University ISBN 978-981-10-6877-5 ISBN 978-981-10-6878-2 (eBook) https://doi.org/10.1007/978-981-10-6878-2 Library of Congress Control Number: 2017955640 Mathematics Subject Classification (2010): 20Cxx, 20C15, 16Gxx, 12E99, 05E10 © Springer Nature Singapore Pte Ltd. 2017 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. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
Preface
This book emerged from a course given twice at Peking University (PKU), each time once a week over two months, while I was visiting the Beijing International Center for Mathematics Research. I essentially taught character theory of finite groups, insisting during the first year on questions of rationality (hence making no assumption for the ground field to be “big enough”). During the second year, I insisted more on applications, and also on related areas, like questions concerning polynomial invariants of finite groups, or the more recent notion of Drinfeld double of a finite group. Throughout the two courses, I tried systematically—but discretely—to help students become familiar with the language of categories. The audience consisted of second-year and third-year students. There are not that many places in the world where you could teach such a material in front of undergraduate students… PKU undergradua
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