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arXiv · 1903.12006

Poisson Principal Bundles

Shahn Majid·Liam Williams
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Abstract

We semiclassicalise the theory of quantum group principal bundles to the level of Poisson geometry. The total space $X$ 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 $q$-Hopf fibration on the standard $q$-sphere. We also construct the Poisson level of the spin connection on a principal bundle.

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Shahn Majid, Liam Williams. 2019-03-28. Poisson Principal Bundles. https://doi.org/10.3842/sigma.2021.006

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