Integrability of central extensions of the Poisson Lie algebra via prequantization
Symplectic Geometry
2021-08-10 v2 Differential Geometry
Abstract
We present a geometric construction of central S^1-extensions of the quantomorphism group of a prequantizable, compact, symplectic manifold, and explicitly describe the corresponding lattice of integrable cocycles on the Poisson Lie algebra. We use this to find nontrivial central S^1-extensions of the universal cover of the group of Hamiltonian diffeomorphisms. In the process, we obtain central S^1-extensions of Lie groups that act by exact strict contact transformations.
Keywords
Cite
@article{arxiv.1508.00841,
title = {Integrability of central extensions of the Poisson Lie algebra via prequantization},
author = {Bas Janssens and Cornelia Vizman},
journal= {arXiv preprint arXiv:1508.00841},
year = {2021}
}
Comments
19 pages. Focus shifted from the full group of exact strict contact transformations to its Lie subgroups