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

The problem of differential calculus on quantum groups