  Three-dimensional bicovariant differential calculus on the quantum group
SU_q(2) is constructed using the approach based on global covariance under the
action of the stabilizing subgroup U(1). Explicit representations of possible
q-deformed Lie algebras are obtained in terms of differential operators. The
consistent gauge covariant differential calculus on SU_q(2) is uniquely
defined. A non-standard Leibnitz rule is proposed for the exterior
differential. The minimal gauge theory with SU_q(2) quantum group symmetry is
considered.
