Coordinates of the quantum plane as q-tensor operators in U-q(su(2)*su(2))

The relation between the set of transformations M(q)(2) of the quantum plane and the quantum universal enveloping algebra U-q(u(2)) is investigated by constructing representations of the factor algebra U-q(u(2)*u(2)). The noncommuting coordinates of M(q)(2), on which U-q(2)*U-q(2) acts, are realized as q-spinors with respect to each U-q(u(2)) algebra. The representation matrices of U-q(2) are constructed as polynomials in these spinor components. This construction allows a derivation of the commutation relations of the noncommuting coordinates of M(q)(2) directly from properties of U-q(u(2)). The generalization of these results to U-q(u(n)) and M(q)(n) is also discussed.