The natural algebraic question of extending a group action on a commutative algebra A of "functions" to a noncommutative algebra of differential (or rational differential, or pseudodifferential) "operators" with coefficients in A is closely related to the study of deformations of A.
In the particular case of homography groups, we will give in this talk an overview of some results about this topic involving transvectants, modular forms and Rankin-Cohen brackets.