In Woronowicz's approach to differential calculi on Hopf algebras, a calculus over an algebra $A$ can be specified by a finite dimensional subspace of the dual of $A$. The best known example is his so-called $3D$-calculus over ${\cal O}_q(SU(2))$. Here the tangent space is spanned by the three elements $q^{-\frac{1}{2}}FK, q^{\frac{1}{2}}EK, (1 - q^{-2})^{-1}(\epsilon - K^4)$.

Now I am interested in the bicovariant calculi over ${\cal O}_q(SU(3))$. I have found an abstract presentation of them for a general coquasitriangular Hopf algebra, but the amount of material I would be required to master before being in a position to understand it is a little off putting. Does anyone know of a more direct presentation, or even better, does anyone know of spanning sets of the tangent spaces corresponding to the calculi?