Modular Representation Theory New Trends and Methods
The aim of this 1983 Yale graduate course was to make some recent results in modular representation theory accessible to an audience ranging from second-year graduate students to established mathematicians. After a short review of background material, thr
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1081
David J. Benson
Modular Representation Theory New Trends and Methods
Second printing
Sprin ger
Author David J. Benson Department of Mathematical Sciences University of Aberdeen Meston Building King's College Aberdeen AB24 SUE Scotland UK
Modular Representation Theory
Library of Congress Cataloging in Publication Data. Benson, David, 1955-. Modular representation theory. (Lecture notes in mathematics; 1081) Bibliography: p. Includes index. 1. Modular representations of groups. 2. Rings (Algebra) I. Title. II. Series: Lecture notes in mathematics (Springer-Verlag); 1081. QA3.L28 no. 1081 [QA171] 510s [512'.2] 84-20207 ISBN 0-387-13389-5 (U.S.)
Mathematics Subject Classification (1980): 20C20
Second printing 2006 ISSN 0075-8434 ISBN-10 3-540-13389-5 Springer-Verlag Berlin Heidelberg New York ISBN-13 978-3-540-13389-6 Springer-Verlag Berlin Heidelberg New York 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, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science-i-Business Media springer.com © Springer-Verlag Berlin Heidelberg 1984 Printed in Germany The use of general descriptive names, registered names, trademarks, 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. Production: LE-T^X Jelonek, Schmidt & Vockler GbR, Leipzig Cover design: design & production GmbH, Heidelberg Printed on acid-free paper
SPIN: 11749158
41/3100/YL
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Introduction This book grew out of a graduate course which I gave at Yale University in the spring semester of 1983. The aim of this course was to make some recent results in modular representation theory accessible to an audience ranging from second-year graduate students to established mathematicians. The material covered has remarkably little overlap with the material currently available in textbook form. The reader new to modular representation theory is therefore encouraged also to read, for example, Feit [51], Curtis and Reiner [37,38], Dornhoff [44], Landrock [65], as well as Brauer*s collected works [16], for rather different angles on the subject. The first of the book's two chapters is intended as background material from the theory of rings and modules. The reader is expected already to be familiar with a large proportion of this, and to refer to the rest as he needs it; proofs are included for the sake of completeness. The second chapter treats three main topics in detail. (i) Representation rings
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