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Infinite dimensional Lie algebras: Representations and applications. (English) Zbl 0593.17014
In these notes, certain infinite-dimensional Lie algebras, the groups to which they correspond, their representations and some of their applications in theoretical physics are described. The topics and treatment were chosen so as to compliment those covered by David Olive (see review above). These algebras occur in relationships between different areas such as: sporadic simple groups in finite group theory; the theory of modular forms; ”completely integrable” dynamical systems; gauge field theory; string theories of elementary particles; conformally invariant field theories; theory of critical phenomena in two-dimensional statistical systems.
Reviewer: L.Vaserstein

MSC:
17B65 Infinite-dimensional Lie (super)algebras
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