This article is cited in 26 papers

Picard groups in Poisson geometry

H. Bursztyn^a, A. Weinstein<sup>b

a</sup> Department of Mathematics, University of Toronto
^b University of California, Berkeley

Abstract: We study isomorphism classes of symplectic dual pairs $P\leftarrow S\rightarrow\overline{P}$, 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 ${\rm Pic}(P)$ under a natural “tensor product” operation. Variants of this construction are also studied, for rings (the origin of the notion of Picard group), Lie groupoids, and symplectic groupoids.

Key words and phrases: Picard group, Morita equivalence, Poisson manifold, symplectic groupoid, bimodule.

MSC: Primary 53D17, 58H05; Secondary 16D90

Received: April 4, 2003

Language: English

DOI: 10.17323/1609-4514-2004-4-1-39-66

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