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On the integration of Poisson homogeneous spaces. (English) Zbl 1156.53051

The problem addressed in the paper under review is that of constructing a symplectic groupoid that integrates a Poisson homogeneous space in a suitable sense. The main theorem applies to quotients of Poisson Lie groups by coisotropic subgroups and the corresponding groupoid is obtained by a reduction procedure starting from the symplectic groupoids constructed by J.-H. Lu and A. Weinstein [C. R. Acad. Sci., Paris, Sér. I 309, No. 18, 951–954 (1989; Zbl 0701.58025)]. The results of the present paper are carefully compared with that of [J.-H. Lu, Poisson geometry in mathematics and physics. Proceedings of the international conference, Tokyo, Japan, June 5–9, 2006. Providence, RI: American Mathematical Society (AMS). Contemporary Mathematics 450, 173-198 (2008; Zbl 1155.53050)].

MSC:

53D05 Symplectic manifolds (general theory)
17B63 Poisson algebras
22A22 Topological groupoids (including differentiable and Lie groupoids)
53D17 Poisson manifolds; Poisson groupoids and algebroids
53D50 Geometric quantization
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References:

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