Infinite-dimensional Lie algebras

Abstract

The present volume exploits the surprising depth of analogy which exists between infinite-dimensional Lie algebras and infinite groups. Broadly speaking, the subject-matter divides into sis sections, spread across eighteen chapters. THe first is the study of subideals, which are analogous to subnormal subgoups, and the related coalescence phenomena. THe second deals with locally nilpotent algebras and the Mal'cev correspondence between groups and Lie algebras. The third discusses finiteness conditions, especially chain conditions. The fourth is a fairly detailed development of properties of finitely generated soluble Lie algebras. Thez fifth gives an infinite-dimensional analogue of the classical structure theory of finite-dimensional Lie algebras. The sixth covers varieties, the finite basis problem, Engel conditions, the theorem of Kostrikin on the restricted Burnside problem, and the recent example of Razmyslov which yields non-nilpotent groups of prime exponent.