PICARD GROUPS IN POISSON GEOMETRY

被引：23
作者：
Bursztyn, Henrique [1 ]
Weinstein, Alan [2 ]
机构：
[1] Univ Toronto, Dept Math, Toronto, ON M5S 3G3, Canada
[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
来源：
MOSCOW MATHEMATICAL JOURNAL | 2004年 / 4卷 / 01期
关键词：
Picard group; Morita equivalence; Poisson manifold; symplectic groupoid; bimodule;
D O I：
10.17323/1609-4514-2004-4-1-39-66
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study isomorphism classes of symplectic dual pairs P <- S -> (P) over bar, 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. Variants of this construction are also studied, for rings (the origin of the notion of Picard group), Lie groupoids, and symplectic groupoids.
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页码：39 / 66
页数：28
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