Hopf-Galois structures on ambiskew polynomial rings

Julien Bichon (1, 2) , Agustín García Iglesias

1 UCA [2017-2020] - Université Clermont Auvergne [2017-2020]
2 LMBP - Laboratoire de Mathématiques Blaise Pascal

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 a generalized ambiskew ring, based on a suitable Hopf algebra H(R). Several examples are examined, including the Hopf-Galois objects over Uq(sl2).

Domaines: Algèbres quantiques [math.QA]; Anneaux et algèbres [math.RA]

Julien Bichon, Agustín García Iglesias. Hopf-Galois structures on ambiskew polynomial rings. Journal of Noncommutative Geometry, 2021, 15 (4), pp.1409-1431. ⟨10.4171/JNCG/441⟩. ⟨hal-02336997⟩