A q-deformed differential calculus at roots of unity

We present main results obtained and published recently, concerning the der ivation satisfying d(N) = 0, and the algebras defined by N-ary relations im posed by such condition. We show the covariant version of this calculus, an d interpret the irreducible parts of the tensorial products of N such diffe rentials in terms of generalized curvature and torsion.