Poisson principal bundles
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Publisher
Journal
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
ISSN
1815-0659
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We semiclassicalise the theory of quantum group principal bundles to the level of Poisson geometry. The total space X
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
q
-Hopf fibration on the standard q
q
-sphere. We also construct the Poisson level of the spin connection on a principal bundle.
Authors
Majid, S; Williams, LCollections
- Mathematics [1468]