Universal Central Extensions of Gauge Algebras and Groups

TL;DR

This paper proves that the canonical central extension of the group of sections of a Lie group bundle over a compact manifold is universal, and extends this result to the corresponding Lie algebra central extension in a broader context.

Contribution

It establishes the universality of the central extension for gauge groups and Lie algebras, generalizing previous constructions and results.

Findings

Proves universality of the central extension of gauge groups.

Extends the universality result to Lie algebra extensions.

Provides a broader setting for the central extension construction.

Abstract

We show that the canonical central extension of the group of sections of a Lie group bundle over a compact manifold, constructed in [NW09], is universal. In doing so, we prove universality of the corresponding central extension of Lie algebras in a slightly more general setting.