Twisted Kähler differential forms

In this paper we construct a twisted analog of the differential graded algebra of Kahler differential forms on a commutative algebra (provided by an endomorphism α). This construction generalizes the work done in (Contemp. Math. 279 (2001) 177–193) for topological purposes. The main feature of this twisted analog is a braiding which is the substitute of the commutativity in the classical situation, in which α is the identity. We show also that the one dimensional difference calculus is a particular case of our construction.