Central extensions of groups of sections
Identifieur interne : 000596 ( Main/Merge ); précédent : 000595; suivant : 000597Central extensions of groups of sections
Auteurs : Karl-Hermann Neeb [Allemagne] ; Christoph Wockel [Allemagne]Source :
- Annals of Global Analysis and Geometry [ 0232-704X ] ; 2009-12-01.
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Abstract
Abstract: If K is a Lie group and q : P → M is a principal K-bundle over the compact manifold M, then any invariant symmetric V-valued bilinear form on the Lie algebra $${\mathfrak{k}}$$ of K defines a Lie algebra extension of the gauge algebra by a space of bundle-valued 1-forms modulo exact 1-forms. In this article, we analyze the integrability of this extension to a Lie group extension for non-connected, possibly infinite-dimensional Lie groups K. If K has finitely many connected components, we give a complete characterization of the integrable extensions. Our results on gauge groups are obtained by the specialization of more general results on extensions of Lie groups of smooth sections of Lie group bundles. In this more general context, we provide sufficient conditions for integrability in terms of data related only to the group K.
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DOI: 10.1007/s10455-009-9168-6
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