Poisson Principal Bundles
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 co...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211182 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Poisson Principal Bundles. Shahn Majid and Liam Williams. SIGMA 17 (2021), 006, 23 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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| ISSN: | 1815-0659 |