Formal symplectic groupoid of a deformation quantization

Abstract

We give a self-contained algebraic description of a formal symplectic groupoid over a Poisson manifold M. To each natural star product on M we then associate a canonical formal symplectic groupoid over M. Finally, we construct a unique formal symplectic groupoid `with separation of variables' over an arbitrary Kaehler-Poisson manifold.

41 page, Lemma 13, several typos and notations corrected

References in corpus (6)

• Deformation quantization of Poisson manifolds, I
• Universality of Fedosov's Construction for Star Products of Wick Type on Pseudo-Kähler Manilfolds
• Natural star products on symplectic manifolds and quantum moment maps
• Formal symplectic groupoid
• On Dequantization of Fedosov's Deformation Quantization
• On the inverse mapping of the formal symplectic groupoid of a deformation quantization

Cited by in corpus (10)

• Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
• The Algebraic Index Theorem and Fedosov Quantization of Lagrange-Finsler and Einstein Spaces
• Fedosov's formal symplectic groupoids and contravariant connections
• On the phase form of a deformation quantization with separation of variables
• Generating functions for local symplectic groupoids and non-perturbative semiclassical quantization
• On Gammelgaard's formula for a star product with separation of variables
• Formal symplectic realizations
• Infinitesimal deformations of a formal symplectic groupoid
• Deformation quantization with separation of variables of an endomorphism bundle
• A heat kernel proof of the index theorem for deformation quantization