Classification of Bicovariant Differential Calculi on Quantum Groups (a Representation-Theoretic Approach)

Abstract

The restricted dual of a quantized enveloping algebra can be viewed as the algebra of functions on a quantum group. According to Woronowicz, there is a general notion of bicovariant differential calculus on such an algebra. We give a classification theorem of these calculi. The proof uses the notion (due to Reshetikhin and Semenov-Tian-Shansky) of a factorizable quasi-triangular Hopf algebra and relies on results of Joseph and Letzter. On the way, we also give a new formula for Rosso's bilinear form.