Abelian extensions via prequantization

Details Abelian extensions via prequantization Abelian extensions via prequantization

2009-10-20

arxiv.org/abs/0910.3906v2

Ann. of Global Analysis and Geometry, 39 (2011) 361-386

Mathematics

Differential Geometry

31 pages, replaced with accepted version

Scientific paper

We generalize the prequantization central extension of a group of diffeomorphisms preserving a closed 2-form \omega (\omega-invariant diffeomorphisms) to an abelian extension of a group of diffeomorphisms preserving a closed vector valued 2-form \omega, up to a linear isomorphism (\omega-equivariant diffeomorphisms). Every abelian extension of a simply connected Lie group can be obtained as the pull-back of such a prequantization abelian extension.

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