Modular Invariant Theory
This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group. It explains a theory that is more complicated than the study of the classical non-modular case, and it describes
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H.E.A. Eddy Campbell r David L. Wehlau
Modular Invariant Theory
H.E.A. Eddy Campbell University of New Brunswick Sir Howard Douglas Hall Dept. Mathematics Bailey Drive 3 Fredericton, New Brunswick Canada E3B 5A3 [email protected]
David L. Wehlau Royal Military College of Canada Dept. Mathematics & Computer Science Kingston, Ontario Canada K7K 7B4 [email protected]
Founding editor of the Encyclopaedia of Mathematical Sciences: Revaz V. Gamkrelidze
ISSN 0938-0396 ISBN 978-3-642-17403-2 e-ISBN 978-3-642-17404-9 DOI 10.1007/978-3-642-17404-9 Springer Heidelberg Dordrecht London New York Mathematics Subject Classification (2010): 13A50 © Springer-Verlag Berlin Heidelberg 2011 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 to prosecution under the German Copyright Law. 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. Cover design: deblik Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
For Diane Mary Brennan, Ian Alexander Brennan, Colin Cameron Brennan, Graham Harold James Brennan and Maggie Orion Cameron. For Charlene Lynn Janeway and Megan Melinda Jane Wehlau.
Preface
At the time we write this book there are several excellent references available which discuss various aspects of modular invariant theory from various points of view: Benson [6]; Derksen and Kemper [26]; Neusel [85]; Neusel and Smith [86]; and Smith [103]. In this book, we concentrate our attention on the modular invariant theory of finite groups. We have included various techniques for determining the structure of and generators for modular rings of invariants, while attempting to avoid too much overlap with the existing literature. An important goal has been to illustrate many topics with detailed examples. We have contrasted the differences between the modular and non-modular cases, and provided instances of our guiding philosophies and analogies. We have included a quick survey of the elements of algebraic geometry and commutative algebra as they apply to invariant theory. Readers who are familiar with these topics may safely skip this chapter. We wish to thank our principal collaborators over the years with whom we have had so much pleasure exploring this fascinating subject: Ian Hughes, Gregor Kemper, R. James Shank, John Harris as well as our students and friends, Jianjun Chuai, Greg Smith, Mike Roth, Br
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