Star products and central extensions

TL;DR

This paper explores how algebra deformations can generate central extensions of loop groups and employs noncommutative geometry to regularize higher-dimensional current algebras for representation construction.

Contribution

It demonstrates the use of algebra deformations for central extensions and applies noncommutative geometry to regularize and represent higher-dimensional current algebras.

Findings

Deformations of smooth function algebras produce nontrivial central extensions of loop groups.

Noncommutative geometry can regularize higher-dimensional current algebras.

Framework for constructing representations of current algebras in higher dimensions.

Abstract

The purpose of the present note is two-fold. First, to show that deformations of algebras of smooth functions can be used to construct topologically nontrivial standard central extensions of loop groups. Second, to use noncommutative geometry as a regularization of current algebras in higher dimensions with the aim of constructing representations of current algebras.