Abelian extensions via prequantization
Differential Geometry
2011-11-17 v2 Symplectic Geometry
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.
Cite
@article{arxiv.0910.3906,
title = {Abelian extensions via prequantization},
author = {Cornelia Vizman},
journal= {arXiv preprint arXiv:0910.3906},
year = {2011}
}
Comments
31 pages, replaced with accepted version