Lie Algebras and Related Topics Proceedings of a Conference Held at
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Lie Algebras and Related Topics Proceedings of a Conference Held at New Brunswick, New Jersey, May 29 - 31, 1981
Edited by D. Winter
Springer-Verlag Berlin Heidelberg New York 1982
Editor David Winter Department of Mathematics University of Michigan Ann Arbor, MI 48109, USA
AMS Subject Classifications (1980): 17 B 05, 17B 50, 17 B 60, 17 B 65, 17 B 70 ISBN 3-540-11563-3 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-11563-3 Springer-Verlag New York Heidelberg Berlin
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1982 Printed in Germany
Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210
Foreword Mathematics related to Lie algebras and Lie groups has flourished in recent years.
We are gaining deep insights into Lie
theoretic phenomena in widely diverse fields at a rapid pace. The 1981 Conference on Lie Algebras and Related Topics, held at Rutgers University, May 29 - 31, brought together over fifty researchers interested in Kac-Moody algebras, Lie algebras of prime characteristic and other Lie theoretic topics. At this conference, twenty-three papers, listed on page 241, were presented.
Most of these papers are included in this volume,
with some in revised form, and many of the others are appearing elsewhere.
Also included in this volume are papers along
related
thematic lines, which were not presented at the conference. A number of very important advances are given in these papers.
To mention just one, Georgia M. Benkart and J. Marshall
Osborn [1] develop the representation theory for rank one simple finite dimensional Lie algebras.
This decisive work enables them,
in a paper to appear elsewhere, to classify all rank one simple finite dimensional Lie algebras, thereby solving a very important problem for the classification theory that has been outstanding for over twenty years. The reader interested in finite dimensional Lie algebras of prime characteristic will find the survey of the classification problem of Richard E. Block [2] very useful.
This excellent survey
is addressed to both beginning researcher and expert, and gives background, statement of the conjecture and a precise and thorough
resume of key results and developments.
In particular, a description
of the known simple finite dimensional Lie algebras is given, semisimple Lie algebras are described in terms of simple Lie algebras in their minimal ideals and the Kostrikin-Safarevic-Kac-Weisfeiler-
IV
Wilson program for classifying simple finite dimensional Lie algebras is outlined. In closing, I want to thank those people who made the 19B1 Conference on Lie Algebras and Rela
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