On the Fedosov Deformation Quantization beyond the Regular Poisson Manifolds

Abstract

A simple iterative procedure is suggested for the deformation quantization of (irregular) Poisson brackets associated to the classical Yang-Baxter equation. The construction is shown to admit a pure algebraic reformulation giving the Universal Deformation Formula (UDF) for any triangular Lie bialgebra. A simple proof of classification theorem for inequivalent UDF's is given. As an example the explicit quantization formula is presented for the quasi-homogeneous Poisson brackets on two-plane.

18 pages, no figures

References in corpus (2)

• Star Product for Second Class Constraint Systems from a BRST Theory
• Wick type deformation quantization of Fedosov manifolds

Cited by in corpus (2)

• BRST quantization of quasi-symplectic manifolds and beyond
• Remarks on generalized Fedosov algebras