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Cohomological classification of deformation quantizations with separation of variables. (English) Zbl 0938.53049
A second cohomology class for the deformation quantization with separation of variables on a Kähler manifold has been calculated. It turns out that for deformation quantizations with separation of variables $$A$$ and $$\overline A$$ the calculation of the Deligne classes $$[\overline A,A]$$ is rather straightforward. The definition of a specific class $$cl$$ based on Deligne’s classes is given and then $$cl(A)$$ is calculated.

##### MSC:
 53D55 Deformation quantization, star products 81S10 Geometry and quantization, symplectic methods 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
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