For any symplectic groupoid$\Sigma$ with base a Poisson manifold$P$ the target map is a symplectic realization of $P$ and the source map is a symplectic realization of the opposite structure. Thus $\Sigma$ with its symplectic structure may be regarded as a desingularization of $P$ with its Poisson structure. Since the symplectic groupoid is the Lie integration of the Poisson Lie algebroid of the Poisson manifold, symplectic realization has been reduced to a problem in Lie theory.

Created on February 12, 2013 at 21:14:46.
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