Invariants of Uq(sℓ(2)) and q-skew derivations Original Research Article

If δ is a q-rmskew derivation of a ring R, then the subring of invariants is R(δ) − r ε R ¦ δ(r) = 0. We prove Theorem. Let δ be a q-skew derivation which is algebraic in its action on the K-algebra R. If R is (σ, δ)-semiprime and I ≠ 0 is a (σ, δ)-stable ideal of R, then I(δ) is a nonnilpotent ideal of R(δ). This result is used to examine the actions of the Hopf algebra H = Uq(sℓ(2)). We show, under certain natural hypotheses, that for any H-stable ideal I ≠ 0 of a semiprime ring, the invariants of I under the action of Uq(sℓ(2)) are nonnilpotent.