The Van den Bergh duality and the modular symmetry of a Poisson variety

摘要: We consider a smooth Poisson affine variety with the trivial canon-ical bundle over \({\mathbb{C}}\). For such deformation quantization algebra \(A_\hbar\) obeys conditions of Van den Bergh duality theorem and corresponding dualizing module is determined by an outer automorphism intrinsic to \(A_\hbar\). show how this can be expressed in terms modular class variety. also prove that free if only structure unimodular.