# Lie Algebras and Related Topics

Share this page *Edited by *
*Georgia M.Benkart; J. Marshall Osborn*

The 1984 classification of the finite-dimensional restricted
simple Lie algebras over an algebraically closed field of
characteristic \(p>7\) provided the impetus for a Special Year
of Lie Algebras, held at the University of Wisconsin, Madison, during
1987-88. Work done during the Special Year and afterward put
researchers much closer toward a solution of the long-standing problem
of determining the finite-dimensional simple Lie algebras over an
algebraically closed field of characteristic \(p>7\).

This volume contains the proceedings of a conference on Lie
algebras and related topics, held in May 1988 to mark the end of the
Special Year. The conference featured lectures on Lie algebras of
prime characteristic, algebraic groups, combinatorics and
representation theory, and Kac-Moody and Virasoro algebras. Many
facets of recent research on Lie theory are reflected in the papers
presented here, testifying to the richness and diversity of this
topic.

# Table of Contents

## Lie Algebras and Related Topics

- Contents vii8 free
- Preface ix10 free
- Conference talks xi12 free
- Abstracts of talks xiii14 free
- Conference participants xxxv36 free
- Isotropic simple Lie algebras of type D4 138 free
- On involutory subalgebras of Kac-Moody Lie algebras 2360
- Structure of certain simple Lie algebras of characteristic three 2764
- Calculus of some functions on the root lattice 3370
- Banach manifolds and their automorphisms associated with groups of type C∞ and D∞ 4380
- The exceptional affine algebra E8(1), triality and chiral algebras 67104
- A characterization of the general Lie algebras of Cartan type W(n: m) 75112
- The 785 conjugacy classes of rational elements of finite order in E8 79116
- The primitives of the continuous linear dual of a Hopf algebra as the dual Lie algebra of a Lie coalgebra 125162
- On irreducible highest weight representations of some affine Lie algebras 177214
- Hyperalgebras, highest weight categories and finite dimensional algebras 203240
- Extensions of representations of semisimple Lie algebras 217254
- Enveloping algebras and division rings for Lie p-algebras 223260
- Serre relations 231268
- The number of irreducible representations of a finite coxeter group 241278
- The role of p-envelopes in the theory of modular Lie algebras 265302
- On modular subalgebras in Lie algebras of prime characteristic 289326
- Cocompact subgroups of semisimple Lie groups 309346