Lie Algebras, Vertex Algebras, and Automorphic Forms

Abstract

Generalized Kac–Moody algebras are natural generalizations of the finite dimensional simple Lie algebras. In important cases their denominator identities are automorphic forms on orthogonal groups. The generalized Kac–Moody algebras with this property can probably be classified and realized as strings moving on suitable spacetimes. In this paper we describe these ideas in more detail.