Fedosov's formal symplectic groupoids and contravariant connections

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.

29 pages

References in corpus (5)

• Universality of Fedosov's Construction for Star Products of Wick Type on Pseudo-Kähler Manilfolds
• Formal symplectic groupoid
• Formal symplectic groupoid of a deformation quantization
• On Dequantization of Fedosov's Deformation Quantization
• A covariant Poisson deformation quantization with separation of variables up to the third order

Cited by in corpus (3)

• Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
• Symplectic Microgeometry III: Monoids
• On the geometry of compatible Poisson and Riemannian structures