G-Systems and Deformation of G-Actions On Rd

Given a (smooth) action of a Lie group G on Rd we construct a DGA whose Maurer-Cartan elements are in one to one correspondence with some class of defomations of the (induced) G-action on the ring of formal power series with coefficients in the ring of smooth functions on Rd. In the final part of this note we discuss the cohomological obstructions to the existence and to the uniqueness (in a sense to be clarified) of such deformations.