Non-Abelian Hopf Cohomology II -- the General Case --

TL;DR

This paper develops a general framework for non-abelian Hopf cohomology, extending classical theories and providing explicit examples and classifications of Hopf torsors.

Contribution

It introduces a comprehensive non-abelian cohomology theory for Hopf algebras with new classifications and explicit computations, generalizing prior work.

Findings

Generalized Serre's non-abelian group cohomology

Established functoriality of the cohomology sets

Classified Hopf torsors

Abstract

We introduce and study non-abelian cohomology sets of Hopf algebras with coefficients in Hopf comodule algebras. We prove that these sets generalize as well Serre's non-abelian group cohomology theory as the cohomological theory constructed by the authors in a previous article. We establish their functoriality and compute explicit examples. Further we classify Hopf torsors.