Integrability and Reduction of Poisson Group Actions 1
نویسنده
چکیده
In this paper we study Poisson actions of complete Poisson groups, without any connectivity assumption or requiring the existence of a momentum map. For any complete Poisson group G with dual G⋆ we obtain a suitably connected integrating symplectic double groupoid S. As a consequence, the cotangent lift of a Poisson action on an integrable Poisson manifold P can be integrated to a Poisson action of the symplectic groupoid S →→G on the symplectic groupoid for P . Finally, we show that the quotient Poisson manifold P/G is also integrable, giving an explicit construction of a symplectic groupoid for it, by a reduction procedure on an associated morphism of double Lie groupoids.
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