We provide necessary and sufficient conditions to extend the Hopf–Galois algebra structure on an algebra to a generalized ambiskew ring based on , 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 . Several examples are examined, including the Hopf–Galois objects over .
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Julien Bichon, Agustín García Iglesias, Hopf–Galois structures on ambiskew polynomial rings. J. Noncommut. Geom. 15 (2021), no. 4, pp. 1409–1431DOI 10.4171/JNCG/441