Covariant central extensions of gauge Lie algebras

TL;DR

This paper classifies covariant central extensions of gauge Lie algebras, focusing on those compatible with transformations of the base manifold, motivated by positive energy representations.

Contribution

It provides a classification of covariant central extensions of gauge Lie algebras under transformation groups, advancing understanding of their structure in mathematical physics.

Findings

Classification of covariant central extensions achieved

Extensions compatible with 1-parameter transformation groups identified

Results relevant for positive energy representation theory

Abstract

Motivated by positive energy representations, we classify those continuous central extensions of the compactly supported gauge Lie algebra that are covariant under a 1-parameter group of transformations of the base manifold.