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

2014/11/21 by Jan Milan Eyni, Eyni, Jan Milan
Mathematics · Medicine · #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #math.GR

paper · pdf · doi:10.48550/arxiv.1411.5851

openalex publication_date 2014/11/21 · arxiv created 2016/03/10 · arxiv updated 2016/03/11 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

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.

Citations

• Differentiable mappings between spaces of sections

Related

• Central Extensions of Gauge Groups Revisited
• Yet another construction of the central extension of the loop group
• Integrating central extensions of Lie algebras via Lie 2-groups
• Lie groups of bundle automorphisms and their extensions
• Universal central extensions of Hom-Lie antialgebras