Hopf-Galois structures on ambiskew polynomial rings.

We provide necessary and sufficient conditions to extend the Hopf-Galois algebra structure on an algebra R to a generalized ambiskew ring based on R, in a way such that the added variables for the extension are skew-primitive in an appropriate sense. We show that the associated Hopf algebra is again a generalized ambiskew ring, based on a suitable Hopf algebra H.R/. Several examples are examined, including the Hopf-Galois objects over U_q(sl₂). [ABSTRACT FROM AUTHOR]