Quadratic Forms in Infinite Dimensional Vector Spaces
For about a decade I have made an effort to study quadratic forms in infinite dimensional vector spaces over arbitrary division rings. Here we present in a systematic fashion half of the results found du ring this period, to wit, the results on denumerab
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Herbert Gross
Progress in math 01
Progress in M a t h e
111
atics
Vol.l: H. Gross, Quadratic Forrns in Iniinite-Dimensional Vector Spaces. XXII, 419 pages. 1979
In preparation: C. Okonek, M. Schneider, H. Spindler, Vector Bundlas on Camplex Projective Spaces This expository treatment of the subject is based on a survey which M. Schneider gave at the Seminaire Bourbaki in November 1978 and on a subsequent course held at the University of Goettingen. It takes into account recent developments and can serve as an introduction to the topical question of Glassilication of holomorphic vector bundlas on complex projective spaces. This has become of interest recently to theoretical physicists because of the relationship with instantons.
K. Diederich, Real Hypersurlaces in cn In this volume, the author gives an expository presentation of the theory of local biholomorphic invariants for real hypersurfaces in cn
Progress in Mathematics
Editedby J. Coates and S. Helgasen
Herbert Gross Quadratic Forms in Infinite Dimensional Vector Spaces
Springer Science+Business Media, LLC
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Author
Herbert Grass Mathematisches Institut Universität Zürich Freiestrasse 36 CH-8032 Zürich Sw1tzerland
Library of Congress Cataloging in Publication Data Grass, Herbert, 19360uadratic forms in infinite-dimensional vector spaces. (Progress in mathematics; 1) lncludes bibliograph1cal references and indexes. 1. Forms, Ouadratic. 2. Vector spaces. I. Title. II. Series: Progress in mathematics (Boston); 1. OA243.G76 512'.33 ISBN 978-1-4757-1456-2 ISBN 978-1-4757-1454-8 (eBook) DOI 10.1007/978-1-4757-1454-8
79-16626
CIP-Kurztitelaufnahme der Deutschen Bibliothek Grass, Herbert: Grass, Herbert: Quadratic forms in infinite dimensional vector spaces I Herbert Grass. (Progress in mathematics; 1) ISBN 978-1-4757-1456-2
All rights reserved. No part of this publ1cation may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electron1c, mechanical, photocopying, recording or otherwise, without pnor permission of the copyright owner. © Springer Science+Business Media New York 1979 Originally published by Birkhäuser Boston 1979 ISBN 978-1-4757-1456-2 Cover design: Albert Gomm SWb/asg, Basel
To Esther
Preface For about a decade I have made an effort to study quadratic forms in infinite dimensional vector spaces over arbitrary division rings. Here we present in a systematic fashion half of the results found during this period, to wit, the results on denumerably infinite spaces ("
~O-
forms") . Certain among the resul ts included here had of course
been published at the time when they were found, others appear for the first time (the case, for example, in Chapters IX, X, XII where I include results contained in the Ph.D.theses by my students
w.
Allenspach,
L. Brand, U. Schneider, M. Studer). If one wants to give an introduction to the geometric algebra of infinite dimensional quadratic spaces, a discussion of ~ 0 -dimensional spaces ideally serves the purpose. First, these spaces show a large nurober of
