Central extensions of groups of sections

Details Central extensions of groups of sections Central extensions of groups of sections

2007-11-21

arxiv.org/abs/0711.3437v2

Ann. Glob. Anal. Geom. 36 (2009) 381

Mathematics

Differential Geometry

54 pages, revised version, to appear in Ann. Glob. Anal. Geom

Scientific paper

10.1007/s10455-009-9168-6

If 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 k of K defines a Lie algebra extension of the gauge algebra by a space of bundle-valued 1-forms modulo exact forms. In the present paper 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 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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