Poisson bracket, deformed bracket and gauge group actions in Kontsevich   deformation quantization
  We 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. 
Dominique Manchon