Differential Calculi on the Quantum Group $SU_q(2)$ and Global $U(1)$-covariance

A variety of three-dimensional left-covariant differential calculi on the quantum group $SU_q(2)$ is considered using an approach based on global $U(1)$ -covariance. Explicit representations of possible $q$-Lie algebras are constructed in terms of differential operators. A gauge covariant differential algebra is uniquely determined. The non-standard Leibnitz rule is obtained for a corresponding $q$-Lie algebra.