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Poisson Principal Bundles
Shahn Majid, Liam Williams School of Mathematical Sciences, Queen Mary University of London, Mile End Rd, London E1 4NS, UK
Аннотация:
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.
Ключевые слова:
noncommutative geometry, quantum group gauge theory, symplectic geometry, Poisson geometry, Lie bialgebra, homogenous space, $q$-monopole.
Поступила: 11 июня 2020 г.; в окончательном варианте 5 января 2021 г.; опубликована 13 января 2021 г.
Образец цитирования:
Shahn Majid, Liam Williams, “Poisson Principal Bundles”, SIGMA, 17 (2021), 006, 23 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1688 https://www.mathnet.ru/rus/sigma/v17/p6
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