Skew Calabi-Yau property of faithfully flat Hopf Galois extensions

Paper

Abstract

This paper shows that if

is a Hopf algebra and

is a faithfully flat

-Galois extension, then

is skew Calabi-Yau provided

and

are. Specifically, for cleft extensions

, the Nakayama automorphism of

can be derived from those of

and

, along with the homological determinant of the

-action on

. This finding is based on the study of the Hopf bimodule structure on