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Fedosov's formal symplectic groupoids and contravariant connections

Alexander V. Karabegov
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Abstract

Using Fedosov's approach we give a geometric construction of a formal symplectic groupoid over any Poisson manifold endowed with a torsion-free Poisson contravariant connection. In the case of Kaehler-Poisson manifolds this construction provides, in particular, the formal symplectic groupoids with separation of variables. We show that the dual of a semisimple Lie algebra does not admit torsion-free Poisson contravariant connections.

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BibTeXRIS

Alexander V. Karabegov. 2005-07-12. Fedosov's formal symplectic groupoids and contravariant connections. https://doi.org/10.1016/j.geomphys.2005.11.004

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