EXTENDED KAC–MOODY ALGEBRAS AND APPLICATIONS

Abstract

We extend the notion of a Kac–Moody algebra defined on the S 1 circle to super Kac–Moody algebras defined on M × G N , M being a smooth closed compact manifold of dimension greater than one, and G N the Grassman algebra with N generators. We compute all the central extensions of these algebras. Then, we determine for each such algebra the derivation algebra constructed from the M × G N diffeomorphisms. The twists of such super Kac–Moody algebras as well as the generalization to noncompact surfaces are partially studied. Finally, we apply our general construction to the study of conformal and superconformal algebras, as well as area-preserving diffeomorphisms algebra and its supersymmetric extension.