Poisson manifolds and their associated stacks

被引：2
|
作者：
Villatoro, Joel [1 ]
机构：
[1] Univ Illinois, Dept Math, 273 Altgeld Hall,1409 W Green St MC 382, Urbana, IL 61801 USA
来源：
LETTERS IN MATHEMATICAL PHYSICS | 2018年 / 108卷 / 03期
关键词：
Poisson manifold; Dirac structure; Lie groupoid; Differentiable stack; Symplectic groupoid; Morita equivalence; BRACKETS;
D O I：
10.1007/s11005-017-1012-5
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We associate to any integrable Poisson manifold a stack, i.e., a category fibered in groupoids over a site. The site in question has objects Dirac manifolds and morphisms pairs consisting of a smooth map and a closed 2-form. We show that two Poisson manifolds are symplectically Morita equivalent if and only if their associated stacks are isomorphic. We also discuss the non-integrable case.
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页码：897 / 926
页数：30
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