Exterior differential algebras and flat connections on Weyl groups

We study some aspects of noncommutative differential geometry on a finite Weyl group in the sense of S. Woronowicz, K. Bresser {\it et al.}, and S. Majid. For any finite Weyl group $W$ we consider the subalgebra generated by flat connections in the left-invariant exterior differential algebra of $W\mathrm{.}$ For root systems of type $A$ and $D$ we describe a set of relations between the flat connections, which conjecturally is a complete set.