Hopf–Galois objects of Calabi–Yau Hopf algebras

Abstract

By using the language of cogroupoids, we show that Hopf–Galois objects of a twisted Calabi–Yau (CY) Hopf algebra with bijective antipode are still twisted CY, and give their Nakayama automorphism explicitly. As applications, cleft Galois objects of twisted CY Hopf algebras and Hopf–Galois objects of the quantum automorphism groups of non-degenerate bilinear forms are proved to be twisted CY.