Picard groups in Poisson geometry

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We study isomorphism classes of symplectic dual pairs P <- S -> P-, where P is an integrable Poisson manifold, S is symplectic, and the two maps are complete, surjective Poisson submersions with connected and simply-connected fibres. For fixed P, these Morita self-equivalences of P form a group Pic(P) under a natural ``tensor product'' operation. We discuss this group in several examples and study variants of this construction for rings (the origin of the notion of Picard group), Lie groupoids, and symplectic groupoids.
26 pages, to appear in special issue of Moscow Math. J. in honor of Pierre Cartier

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Symplectic Geometry, Differential Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/66979

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0304048
 http://arxiv.org/abs/math/0304048
 Moscow Math. J. 4 (2004), no. 1, 39-66.

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arXiv