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The variant of Fedosov construction based on fairly general fiberwise product in the Weyl bundle is studied.
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A. Cattaneo, G. Felder, and L Tomassini, From local to global deformation quantization of Poisson manifolds, Duke Math. J. 115
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V.A. Dolgushev, A.P. Isaev, S.L. Lyakhovich and A.A. Sharapov, On the Fedosov deformation quantization beyond the regular Poisson manifolds, Nucl.Phys. B645
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