Homological smoothness of Hopf-Galois extensions

TL;DR

This paper proves that the homological smoothness of a Hopf-Galois extension is preserved from the base algebra and the Hopf algebra to the total algebra, under certain conditions.

Contribution

It establishes that homological smoothness is maintained in Hopf-Galois extensions when both the Hopf algebra and the base algebra are homologically smooth.

Findings

Homological smoothness of $A$ follows from that of $H$ and $B$.

The result applies to faithfully flat $H$-Galois extensions with bijective antipode.

Provides conditions under which homological properties are preserved in algebra extensions.

Abstract

We show that if $H$ is a Hopf algebra with bijective antipode and $B \subset A$ is a faithfully flat $H$-Galois extension, then $A$ is homologically smooth if $H$ and $B$ are.