On quantization of the polynomial symplectomorphisms

It will be considered a construction of pull-back of the polynomial symplectomorphisms of an affine space of an even dimension to automorphisms of the corresponding Weyl algebra. It has been proposed by authors jointly with J.-T. You in https://arxiv.org/abs/1812.02859. The construction provides a positive solution to the Kontsevich conjecture on isomorphism between the automorphism groups of the Weyl and Poisson algebras in zero characteristic. We also will discuss the relation between the Kontsevich conjecture and the problem of Jacobian.