Abelian extensions via prequantization

Abstract

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.