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In this paper the local differential calculus over Fedosov algebra is constructed using the trivialization isomorphism.
M. Spivak ”Calculus on manifolds” , Addison-Wesley, 1965
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C. Emmrich, A. Weinstein ”The differential geometry of Fedosov’s quantization” in J.-L. Brylinski, R. Brylinski, V. Guillemin, V. Kac (Eds.) Lie Theory and Geometry. In Honor of Bertram Kostant , Progr. Math. 1994, Birkhäuser, (hep-th/9311094)
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B.V. Fedosov ”A simple geometrical construction of deformation quantization” , J. Diff. Geom. 40
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B. V. Fedosov ”Deformation quantization and index theory” , Akademie Verlag, Berlin, 1996
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M. Reuter ”Noncommutative geometry on quantum phase space” , Int. J. Mod. Phys. A 11
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I. Gelfand, V. Retakh, M. Shubin ”Fedosov manifolds” , Adv. Math. 136
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J. Madore ”An introduction to noncommutative differential geometry and its physical applications” , Cambridge University Press, 1999
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N. Seiberg, E. Witten ”String theory and noncommutative geometry” , JHEP 09 (1999) 032
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M. Dubois-Violette ”Lectures on Graded Differential Algebras and Noncommutative Geometry” , qa/9912017
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T. Asakawa, I. Kishimoto ”Noncommutative gauge theories from deformation quantization” , Nucl. Phys. B 591
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V.A. Dolgushev, S.L. Lyakhovich, A.A. Sharapov ”Wick type deformation quantization of Fedosov manifolds” , Nucl. Phys. B 606
2001
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S. Waldmann ”Morita equivalence of Fedosov star products and deformed hermitian vector bundles” , Lett. Math. Phys. 60
2002
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M. Gadella, M. A. del Olmo, J. Tosiek ”Geometrical origin of the ∗ * -product in the Fedosov formalism” , J. Geom. Phys. 55
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