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

The relation between the set of transformations M{sub q}(2) of the quantum plane and the quantum universal enveloping algebra U{sub q}(u(2)) is investigated by constructing representations of the factor algebra U{sub q} (u(2) * u(2)). The non-commuting coordinates of M{sub q}(2), on which U{sub q}(2) * U{sub q}(2) acts, are realized as q-spinors with respect to each U{sub q}(u(2)) algebra. The representation matrices of U{sub 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{sub q}(2) directly from properties of U{sub q}(u(2)). The generalization of these results to U{sub q}(u(n)) and M{sub q}(n) is also discussed.