A differential calculus on the quantum group $SU_q(2)$ compatible with the gauge-transformation structure

We consider a three-dimensional bicovariant differential calculus on the quantum group $SU_q(2)$ that is compatible with the structure of gauge transformations. In the approach based on the global covariance with respect to the stability subgroup $U(1)$, we show that the gauge-covariant exterior differential algebra on $SU_q(2)$ is uniquely determined. We construct explicit representations of $q$-deformed Lie algebras in terms of differential operators.