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On the Fedosov Deformation Quantization beyond the Regular Poisson Manifolds

V. A. Dolgushev·A. P. Isaev·S. L. Lyakhovich·A. A. Sharapov
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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.

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V. A. Dolgushev, A. P. Isaev, S. L. Lyakhovich, A. A. Sharapov. 2002-06-05. On the Fedosov Deformation Quantization beyond the Regular Poisson Manifolds. https://doi.org/10.1016/s0550-3213(02)00763-0

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