The Jordan structure of Lie and Kac-Moody algebras

Abstract

The authors establish a precise relation between the structures of Lie and Jordan algebras by presenting a method of constructing one type of algebra from the other. The examples of the Lie algebras associated to simple Jordan algebras Mm(n) and Clifford algebras are discussed in detail. The generalization of such arguments to infinite-dimensional Lie algebras in terms of Fermi fields is also discussed.