Regularization and Quantization of Higher Dimensional Current Algebras

Abstract

We present some recently discovered infinite dimensional Lie algebras that can be understood as extensions of the algebra Map(M,g) of maps from a compact p-dimensional manifold to some finite dimensional Lie algebra g. In the first part of the paper, we describe the physical motivations for the study of these algebras. In the second part, we discuss their realization in terms of pseudo-differential operators and comment on their possible representation theory.