Cohomological classification of deformation quantizations with separation of variables (Q1392679)

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.