Equivariant Hopf Galois extensions and Hopf cyclic cohomology

TL;DR

This paper introduces equivariant Hopf Galois extensions, expanding the framework for associating SAYD modules to Hopf algebra extensions and generalizing previous results in the field.

Contribution

It defines equivariant Hopf Galois extensions and demonstrates their role as functors between categories of SAYD modules, extending prior work on Hopf Galois extensions.

Findings

Generalizes Jara-Stefan and B"ohm-Stefan results

Establishes functorial relationship between SAYD modules and extensions

Provides a new framework for Hopf cyclic cohomology

Abstract

We define the notion of equivariant Hopf Galois extension and apply it as a functor between category of SAYD modules of the Hopf algebras involving in the extension. This generalizes the result of Jara-Stefan and B\"ohm-Stefan on associating a SAYD modules to any ordinary Hopf Galois extension.