Composition Algebras
In this chapter we present the basic theory of composition algebras and determine their structure. Since these are (not necessarily associative) algebras with quadratic norms, we need some fundamental parts of the theory of quadratic forms, which we there
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Springer Monographs in Mathematics
Springer-Verlag Berlin Heidelberg GmbH
Tonny A. Springer • Ferdinand D. Veldkamp
Octonions, Jordan Algebras and Exceptional Groups
,
Springer
Tonny A. Springer
Mathematisch Instituut Budapestlaan 6 3584 CD Utrecht, The Netherlands e-mail: [email protected]
Perdinand D. Veldkamp t
Library of Congress Cataloging-in-Publication Data Springer, T. A. (Tonny Albert), 1926Octonions, Iordan algebras and exceptional groups I Tonny A. Springer, Ferdinand D. Veldkamp. p. cm. -- (Springer monographs in mathematics) "[Revised] EngIish version of the original German notes"--Pref. Includes bibliographical references and index. ISBN 978-3-642-08563-5 ISBN 978-3-662-12622-6 (eBook) DOI 10.1007/978-3-662-12622-6 l.lordan algebras. 2. Alternative rings. 3. Linear algebraic groups. I.Veldkamp, Ferdinand D., 1931-1999. Il. Title.lII. Series. QA252.5 .S69 2000 512'.24--dc21
00-021741
Mathematics Subject Classification (1991): 17 C 50, 17 DOS, 20 G 15
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Preface
In the summer of 1963, T.A. Springer gave a course of lectures at the Mathematical Institute of G6ttingen University on the theory of octonion and Jordan algebras and some exceptional groups related to these. Notes were written by Peter Eysenbach and these were published in mimeographed form by the G6ttingen Institute under the title "Oktaven, lordan-Algebren und Ausnahmegruppen" ([Sp 63] in the references at the end of this book). For a considerable part the results exposed in these lectures were not new, but they were brought in greater generality, with new proofs or with a different approach. New features were the introduction of twisted composition algebras, and their use in the description of exceptional Jordan division algebras. The G6ttingen notes shared the fate of so many mimeographed lecture notes: to bec
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