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.
Isotropic simple Lie algebras of type $D 4$ by B. N. Allison On involutory subalgebras of Kac-Moody Lie algebras by S. Berman Structure of certain simple Lie algebras of characteristic three by G. Brown Calculus of some functions on the root lattice by R. W. Deckhart Banach manifolds and their automorphisms associated with groups of type $C \infty$ and $D \infty$ by J. Dorfmeister, E. Neher, and J. Szmigielski The exceptional affine algebra $E 8^(1)$, triality and Chiral algebras by A. J. Feingold, I. B. Frenkel, and J. F. X. Ries A characterization of the general Lie algebras of Cartan type $W(n:\underline\underline m)$ by T. B. Gregory The 785 conjugacy classes of rational elements of finite order in $E 8$ by W. G. McKay, R. V. Moody, J. Patera, and A. Pianzola The primitives of the continuous linear dual of a Hopf algebra as the dual Lie algebra of a Lie coalgebra by E. Michaelis On irreducible highest weight representations of some affine Lie algebras by K. C. Misra Hyperalgebras, highest weight categories and finite dimensional algebras by B. J. Parshall Extensions of representations of semisimple Lie algebras by J. G. Ryan Enveloping algebras and division rings for Lie $p$-algebras by J. Schue Serre relations by P. E. Singer The number of irreducible representations of a finite coxeter group by L. Solomon The role of $p$-envelopes in the theory of modular Lie algebras by H. Strade On modular subalgebras in Lie algebras of prime characteristic by V. R. Varea Cocompact subgroups of semisimple Lie groups by D. Witte.