Bicovariant differential calculus on quantum groups SUq(N) and SOq(N)

Following Woronowicz's proposal the bicovariant differential calculus on the quantum groups SUq(N) and SOq(N) is constructed. A systematic construction of bicovariant bimodules by using the Rq matrix is presented. The relation between the Hopf algebras generated by the linear functionals relating the left and right multiplication of these bicovariant bimodules, and the q-deformed universal enveloping algebras is given. Imposing the conditions of bicovariance and consistency with the quantum group structure the differential algebras and exterior derivatives are defined. As an application the Maurer-Cartan equations and the q-analogue of the structure constants are formulated. (orig.)