Representation Theory of the Virasoro Algebra
The Virasoro algebra is an infinite dimensional Lie algebra that plays an increasingly important role in mathematics and theoretical physics. This book describes some fundamental facts about the representation theory of the Virasoro algebra in a self-cont
- PDF / 4,911,872 Bytes
- 482 Pages / 439.37 x 666.142 pts Page_size
- 97 Downloads / 232 Views
For further volumes: www.springer.com/series/3733
Kenji Iohara r Yoshiyuki Koga
Representation Theory of the Virasoro Algebra
Kenji Iohara Université Claude Bernard Lyon 1 Institut Camille Jordan 43 Boulevard du 11 Novembre 1918 69622 Villeurbanne Cedex France [email protected]
Yoshiyuki Koga University of Fukui Department of Applied Physics Faculty of Engineering 3-9-1 Bunkyo 910-8507 Fukui Japan [email protected]
ISSN 1439-7382 e-ISBN 978-0-85729-160-8 ISBN 978-0-85729-159-2 DOI 10.1007/978-0-85729-160-8 Springer London Dordrecht Heidelberg New York British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Mathematics Subject Classification (2010): 17B10, 17B50, 17B55, 17B67, 17B68, 17B69, 17B70, 81R10 © Springer-Verlag London Limited 2011 Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publishers. The use of 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 laws and regulations and therefore free for general use. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. Cover design: VTEX, Vilnius Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedicated to Professor Michio Jimbo on the occasion of his sixtieth birthday.
Preface
The Virasoro algebra is an infinite dimensional Lie algebra which has appeared in several context. For example, E. Cartan [C] in 1909 classified simple infinite dimensional linearly compact Lie algebras over C which contains the Lie algebra W m of all formal vector fields in m determinates. Around 1940, the Lie algebra of derivations of the group algebra of Z/pZ over a field of characteristic p > 2 was studied by colleagues of E. Witt, e.g., H. Zassenhaus [Za] showed that this Lie algebra is simple and H.J. Chang [Ch] studied its representations. All these works treated the so-called Witt algebra, or the centreless Virasoro algebra. It was only in 1966 that its non-trivial central extension first appeared in the work of R. Block [Bl] over a field of positive characteristic in classifying certain class of Lie algebras. In 1968, I. M. Gelfand and D. B. Fuchs [GF] determined the cohomology ring of the Lie algebra of the vector fields on the circle. In 1970, the Virasoro algebra appeared in the article [Vir] of M. Vira
Data Loading...
