6533b85ffe1ef96bd12c1a73

RESEARCH PRODUCT

Structure of Kac-Moody groups

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For a phys ic i s t , a Kac-Moody algebra is the current algebra of a quantum f i e l d theory model in I + I space-time dimensions with an in terna l symmetry group G [ I ] . A More p rec ise ly , l e t ~ be the Lie algebra of G . The Kac-Moody algebra g is a one-dimensional central extension of the loop algebra Map(S I , g ) . I f f l ' f2 C Map(S I ,~ ) , then the commutator is defined point -wise,