Regularization and Quantization of Higher Dimensional Current Algebras

TL;DR

This paper explores new infinite-dimensional Lie algebras extending current algebras, motivated by physical theories, and discusses their realization via pseudo-differential operators and potential representations.

Contribution

It introduces and analyzes new classes of infinite-dimensional Lie algebras as extensions of current algebras, with insights into their realizations and representation theory.

Findings

Identification of new infinite-dimensional Lie algebras

Realization through pseudo-differential operators

Discussion on potential representation theory

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.