Non-abelian Hopf Cohomology of Radford products

TL;DR

This paper develops a framework for understanding the non-abelian Hopf cohomology of Radford products, providing explicit computations and an exact sequence relating the cohomology of the product to its factors.

Contribution

It introduces a method to express the cohomology of Radford products in terms of their factors and derives an exact sequence to facilitate computations.

Findings

Cohomology sets can be expressed via factors' cohomology.

An exact sequence relates Radford product cohomology to its factors.

Explicit computations are possible in large classes of examples.

Abstract

We study the non-abelian Hopf cohomology theory of Radford products with coefficients in a comodule algebra. We show that these sets can be expressed in terms of the non-abelian Hopf cohomology theory of each factor of the Radford product. We write down an exact sequence relating these objects. This allows to compute explicitly the non-abelian Hopf cohomology sets in large classes of examples.