2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58792We express the difference between Poisson bracket and deformed bracket for Kontsevich deformation quantization on any Poisson manifold by means of second derivative of the formality quasi-isomorphism. The counterpart on star products of the action of formal diffeomorphisms on Poisson formal bivector fields is also investigated.11 pages, one xypic figure. Minor changes on section IVQuantum AlgebraAlgebraic Geometry16S80; 53D17; 53D55; 58A50Poisson bracket, deformed bracket and gauge group actions in Kontsevich deformation quantizationtext