We study some aspects of noncommutative differential geometry on a finite Weyl group in the sense of S. Woronowicz, K. Bresser 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.
For root systems of type A and D we describe a set of relations between the flat connections, which conjecturally is a complete set.