Generalized deformations and Hochschild cohomology

We present a generalization of Gerstenhaber's theory of deformations. We no longer assume that the deformation parameter t acts in its usual free and symmetric way on the elements of the original algebra A, but in the followi ng manner: t . a = sigma (a)t and a . t = tau (a)t, where sigma and tau are endomorphisms of A. We develop the cohomological framework adapted to thes e deformations.