The Minnesota Notes on Jordan Algebras and Their Applications
This volume contains a re-edition of Max Koecher's famous Minnesota Notes. The main objects are homogeneous, but not necessarily convex, cones. They are described in terms of Jordan algebras. The central point is a correspondence between semisimple real J
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1710
Lecture Notes in Mathematics Editors: A. Dold, Heidelberg F. Takens, Groningen B. Teissier, Paris
1710
Springer Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo
Max Koecher
The Minnesota Notes on Jordan Algebras and Their Applications Edited and annotated by Aloys Krieg and Sebastian Walcher
Springer
Author Max Koecher t Editors Aloys Krieg Lehrstuhl A fur Mathematik RWTHAachen D-52056 Aachen, Germany E-mail: [email protected] Sebastian Walcher Zentrum Mathematik TU MUnchen D-80290 Munchen, Germany E-mail: [email protected] Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Koecher, Max: The Minnesota notes on Jordan Algebras and their applications I Max Koecher. Ed. and an not. by Aloys Krieg and Sebastian Walcher. - Berlin; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris; Singapore; Tokyo: Springer. 1999 (Lecture notes in mathematics; 1710) ISBN 3-540-66360-6
The material of this volume was originally published in 1962 under the title "Jordan Algebras and Their Applications" by the School of Mathematics of the University of Minnesota. Mathematics Subject Classification (1991): 17C36, I7C55, 32M 15, 32N 10, 43A85, 17-02,22-99 ISSN 0075-8434 ISBN 3-540-66360-0 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, speci fically the rights of translation, reprinti ng, re-use of illustrations, recitation, broadcasting, reproduction on microfilms 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-Verlag. Violations are liable for prosecution under the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1999 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. Typesetting: Camera-ready TEX output by the editors SPIN: 10650255
4J13143-543210 - Printed on acid-free paper
Preface
These notes contain the material of lectures on Jordan algebras given by me at the University of Minnesota during the academic year 1961-62. I tried to make use of the algebraic structure of a Jordan algebra over the field of real resp. complex numbers in certain applications to analysis. In the center of the investigatons stands the bijective correspondence between semisimple real Jordan algebras and the so-called w-domains. This correspondence was known for domains of positivity. Most of the material is taken from an unpublished manuscript written jointly with E. Artin and H. Braun. I wish to express my thanks to my friends and colleagues E. Calabi, H. Rohrl
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