Lie Algebras, Madison 1987 Proceedings of a Workshop held in Madison
During the academic year 1987-1988 the University of Wisconsin in Madison hosted a Special Year of Lie Algebras. A Workshop on Lie Algebras, of which these are the proceedings, inaugurated the special year. The principal focus of the year and of the works
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1373 Georgia Benkart J. Marshall Osborn (Eds.)
Lie Algebras, Madison 1987 Proceedings of a Workshop held in Madison, Wisconsin, August 23-28, 1987
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong
Editors
Georgia Benkart
J. Marshall Osborn Department of Mathematics, University of Wisconsin Madison, WI 53706-1388, USA
Mathematics Subject Classification (1980): Primary: 17B20, 17B50, 17B67 Secondary: 16A61, 17B56, 17B65, 18G 15 ISBN 3-540-51147-4 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-51147-4 Springer-Verlag New York Berlin Heidelberg
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© Springer-Verlag Berlin Heidelberg 1989 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210
Preface
During the academic year 1987-1988 the University of Wisconsin, Madison hosted a Special Year of Lie Algebras. A Workshop on Lie Algebras, of which these are the proceedings, inaugurated the special year. The principal focus of the year and of the workshop was the long-standing problem of classifying the simple finite dimensional Lie algebras over algebraically closed fields of prime characteristic. However, other lectures at the workshop dealt with the related areas of algebraic groups, representation theory, and Kac-Moody Lie algebras. The titles of the fourteen papers presented at the workshop can be found at the end, followed by a list of the participants in the workshop and their addresses. Nine of these papers, (eight research articles and one expository article), comprise this volume. The first paper, by Strade, develops the notion of the absolute toral rank of a modular Lie algebra. This new concept combines earlier approaches of Block-Wilson and Benkart-Osborn, and it seems to playa critical role in determining the structure of simple Lie algebras of prime characteristic. The next three papers investigate various topics related to the classification problem: embeddings of generalized Witt algebras; isomorphism classes of Hamiltonian Lie algebras; and Lie algebras with subalgebras of codimension one and their relationship to forms of Zassenhaus Lie algebras. The determination of the restricted simple Lie algebras over algebraically closed fields of prime characteristic has been accomplished recently by Block and Wilson. Serconek and Wilson use this result as the starting point for their discussion of forms of restricted simple algebras. In the next paper Varea employs the classification of the rank one simple Lie algebras to inv
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