Steinberg Groups for Jordan Pairs
Steinberg groups, originating in the work of R. Steinberg on Chevalley groups in the nineteen sixties, are groups defined by generators and relations. The main examples are groups modelled on elementary matrices in the general linear, orthogonal and sympl
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Ottmar Loos Erhard Neher
Steinberg Groups for Jordan Pairs
Progress in Mathematics Volume 332
Series Editors Antoine Chambert-Loir, Université Paris-Diderot, Paris, France Jiang-Hua Lu, The University of Hong Kong, Hong Kong SAR, China Michael Ruzhansky, Imperial College, London, UK Yuri Tschinkel, Courant Institute of Mathematical Sciences, New York, USA
More information about this series at http://www.springer.com/series/4848
Ottmar Loos • Erhard Neher
Steinberg Groups for Jordan Pairs
Ottmar Loos Fakultät für Mathematik und Informatik FernUniversität in Hagen Hagen, Germany
Erhard Neher Department of Mathematics and Statistics University of Ottawa Ottawa, ON, Canada
ISSN 2296-505X (electronic) ISSN 0743-1643 Progress in Mathematics ISBN 978-1-0716-0262-1 ISBN 978-1-0716-0264-5 (eBook) https://doi.org/10.1007/978-1-0716-0264-5 Mathematics Subject Classification (2010): 05C20, 05C63, 11E57, 17B22, 17B60, 17Cxx, 17C27, 17C30, 17C50, 19Cxx, 19C09, 20E42, 20H25 © Springer Science+Business Media, LLC, part of Springer Nature 2019 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. This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Science+Business Media, LLC The registered company address is: 233 Spring Street, New York, NY 10013, U.S.A.
Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii
Notation and Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi
Chapter I. Groups with commutator relations . . . . . . . . . . . . . . . . . . . . . . . . .
1
Nilpotent sets of roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reflection systems and root systems . . . . . . . . . . . . . . . . . . . . . . . . Groups with commutator rela
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