TO SUPERANAL YSIS Edited by A. A. KIRILLOV Translated from the Russian
by J. Niederle and R. Kotecky English translation edited and revised by
Dimitri Leites SPRINGER-SCIENCE+BUSINESS MEDIA, B. V. Library of
Congress Cataloging-in-Publication Data Berezin, F. A. (Feliks
Aleksandrovich) Introduction to superanalysis. (Mathematical physics and
applied mathematics; v. 9) Part I is translation of: Vvedenie v algebru
i analiz s antikommutirurushchimi peremennymi. Bibliography: p. Includes
index. 1. Mathetical analysis. I. Title. II. Title: Superanalysis. III.
Series. QA300. B459 1987 530. 15'5 87-16293 ISBN 978-90-481-8392-0 ISBN
978-94-017-1963-6 (eBook) DOI 10. 1007/978-94-017-1963-6 All Rights
Reserved (c) 1987 by Springer Science+Business Media Dordrecht
Originally published by D. Reidel Publishing Company, Dordrecht, Holland
in 1987 No part of the material protected by this copyright notice may
be reproduced in whole or in part or utilized in any form or by any
means electronic or mechanical including photocopying recording or
storing in any electronic information system without first obtaining the
written permission of the copyright owner. CONTENTS EDITOR'S FOREWORD ix
INTRODUCTION 1 1. The Sources 1 2. Supermanifolds 3 3. Additional
Structures on Supermanifolds 11 4. Representations of Lie Superalgebras
and Supergroups 21 5. Conclusion 23 References 24 PART I CHAPTER 1.
GRASSMANN ALGEBRA 29 1. Basic Facts on Associative Algebras 29 2.
Grassmann Algebras 35 3. Algebras A(U) 55 CHAPTER 2. SUPERANAL YSIS
74 1. Derivatives 74 2. Integral 76 CHAPTER 3. LINEAR ALGEBRA IN
Zz-GRADED SPACES 90 1.
