Hopf Galois (Co)Extensions In Noncommutative Geometry

TL;DR

This paper presents a new proof connecting Hopf Galois coextensions of coalgebras to stable anti Yetter-Drinfeld modules and demonstrates an isomorphism between two related cohomology theories.

Contribution

It introduces an alternative proof using Hopf algebra tools and establishes the isomorphism between two cohomology theories in the context of Hopf Galois coextensions.

Findings

Hopf Galois coextensions are sources of stable anti Yetter-Drinfeld modules

Two cohomology theories related to these coextensions are isomorphic

Provides a new proof approach using Hopf algebra tools

Abstract

We introduce an alternative proof, with the use of tools and notions for Hopf algebras, to show that Hopf Galois coextensions of coalgebras are the sources of stable anti Yetter-Drinfeld modules. Furthermore we show that two natural cohomology theories related to a Hopf Galois coextension are isomorphic.