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Deformation quantizations with separation of variables on a Kähler manifold

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We give a simple geometric description of all formal differentiable deformation quantizations on a Kähler manifoldM such that for each open subsetUM ⋆-multiplication from the left by a holomorphic function and from the right by an antiholomorphic function onU coincides with the pointwise multiplication by these functions. We show that these quantizations are in 1-1 correspondence with the formal deformations of the original Kähler metrics onM.

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Communicated by H. Araki

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Karabegov, A.V. Deformation quantizations with separation of variables on a Kähler manifold. Commun.Math. Phys. 180, 745–755 (1996). https://doi.org/10.1007/BF02099631

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  • DOI: https://doi.org/10.1007/BF02099631

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