2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64396We give a simple formula for the operator C_3 of the standard deformation quantization with separation of variables on a Kähler manifold M. Unlike C_1 and C_2, this operator can not be expressed in terms of the Kähler-Poisson tensor on M. We modify C_3 to obtain a covariant deformation quantization with separation of variables up to the third order which is expressed in terms of the Poisson tensor on M and thus can be defined on an arbitrary complex manifold endowed with a Poisson bivector field of type (1,1).9 pages, minor typos correctedQuantum Algebra53D55; 53C55text