Fedosov's formal symplectic groupoids and contravariant connections

Details Fedosov's formal symplectic groupoids and contravariant connections Fedosov's formal symplectic groupoids and contravariant connections

2005-07-12

arxiv.org/abs/math/0507244v1

Mathematics

Quantum Algebra

29 pages

Scientific paper

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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