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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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