q-Deformed SU(2) instantons by q-quaternions

Interpreting the coordinates of the quantum Euclidean space R-q(4) [the SOq(4)-covariant noncommutative space] as the entries of a "q-quaternion matrix" we construct (anti) instanton solutions of a would-be q-deformed su(2) Yang-Mills theory on R-q(4). Since the (anti) selfduality equations are covariant under the quantum group of deformed rotations, translations and scale change, by applying the latter we can respectively generate "gauge equivalent" or "inequivalent" solutions from the one centered at the origin and with unit size. We also construct multi-instanton solutions. As these solutions depend on noncommuting parameters playing the roles of 'sizes' and 'coordinates of the centers' of the instantons, this indicates that the moduli space of a complete theory should be a noncommutative manifold. Similarly, as the (global) gauge transformations relating "gauge equivalent" solutions depend on the generators of two copies of SUq(2), this suggests that gauge transformations should be allowed to depend on additional noncommutative parameters.