The bicovariant differential calculi on quantum groups of Woronowicz have the drawback that their dimensions do not agree with that of the corresponding classical calculus. In this paper we discuss the first-order differential calculus which arises from a simple quantum Lie algebra. This calculus has the correct dimension and is shown to be bicovariant and complete. But it does not satisfy the Leibniz rule. For sl_n this approach leads to a differential calculus which satisfies a simple generalization of the Leibniz rule.

Contribution to the proceedings of the Colloquium on Quantum Groups and Integrable Systems Prague, June 1996. amslatex, 9 pages. For related information see http://www.mth.kcl.ac.uk/~delius/q-lie.html