Poisson Principal Bundles
Quantum Algebra
2021-01-14 v3 Differential Geometry
Abstract
We semiclassicalise the theory of quantum group principal bundles to the level of Poisson geometry. The total space is a Poisson manifold with Poisson-compatible contravariant connection, the fibre is a Poisson-Lie group in the sense of Drinfeld with bicovariant Poisson-compatible contravariant connection, and the base has an inherited Poisson structure and Poisson-compatible contravariant connection. The latter are known to be the semiclassical data for a quantum differential calculus. The theory is illustrated by the Poisson level of the -Hopf fibration on the standard -sphere. We also construct the Poisson level of the spin connection on a principal bundle.
Cite
@article{arxiv.1903.12006,
title = {Poisson Principal Bundles},
author = {Shahn Majid and Liam Williams},
journal= {arXiv preprint arXiv:1903.12006},
year = {2021}
}