Universal central extensions for groups of sections on non-compact manifolds

TL;DR

This paper constructs a universal central Lie group extension for sections of Lie group bundles over non-compact manifolds, extending previous results that required compact base manifolds.

Contribution

It generalizes existing theories of central extensions from compact to non-compact base manifolds for Lie group bundles and their sections.

Findings

Constructed a central Lie group extension for non-compact base manifolds.

Proved the universality of this extension.

Extended previous compact manifold results to non-compact cases.

Abstract

We construct a central Lie group extension for the Lie group of compactly supported sections of a Lie group bundle over a sigma-compact base manifold. This generalises a result of the paper "Central extensions of groups of sections" by Neeb and Wockel, where the base manifold is assumed to be compact. In the second part of the paper, we show that this extension is universal and obtain a generalisation of a corresponding result in the paper "Universal central extensions of gauge algebras and groups" by Janssens and Wockel, where again (in the case of Lie group extensions) the base manifold is assumed compact.