On the structure of a differential algebra used by Connes and Lott

We investigate the structure of a differential algebra associated with the simplest twopoint K-cycle used by Connes and Lott for physical model building. We show that, in this case, the factorization of the universal differential algebra with respect to the canonical ideal can be performed explicitly. This enables us to present a complete analysis of the structure of the differential algebra under investigation, including explicit multiplication and differentiation rules. Moreover, we get explicit formulae for the scalar product, induced by the Dixmier trace, of elements of the differential algebra of arbitrary degree.