We generalize the notion, due to H. Cartan, of an operation of a Lie algebra in a graded differential algebra. Firstly, for such an operation we give a natural extension to the universal enveloping algebra of the Lie algebra and analyze all of its properties. Building on this we define the notion of an H-operation, thai is the operation of a general Hopf algebra H in a graded differential algebra. We then introduce for such an operation the notion of algebraic connection. Finally we discuss the corresponding noncommutative version of the Weil algebra as the universal initial object of the category of H-operations with connections.