SKEW DERIVATIONS AND UQ(SL(2))

This note first describes the basic properties of the skew derivations on the polynomial ring k[X]. As a consequence of these properties it is proved that the q-analogue of the enveloping algebra of sl(2), U(q)(sl(2)), has a unique action on C[X], where "action" means that C[X] is a module algebra in the Hopf algebra sense. This depends on the fact that the generators of a subalgebra of U(q)(sl(2)) described by Woronowicz must act via an automorphism, and the skew derivations associated to it.