THE PROBLEM OF DIFFERENTIAL-CALCULUS ON QUANTUM GROUPS

The bicovariant differential calculi on quantum groups of Woronowicz h ave the drawback that their dimensions do not agree with that of the c orresponding classical calculus. In this paper we discuss the first-or der differential calculus which arises from a simple quantum Lie algeb ra l(h)(g). This calculus has the correct dimension and is shown to be bicovariant and complete. But it does not satisfy the Leibniz rule. F or sl(n) this approach leads to a differential calculus which satisfie s a simple generalization of the Leibniz rule.