Representations of the category of modules over pointed Hopf algebras over S_3 and S_4

TL;DR

This paper classifies indecomposable module categories over certain Hopf algebra representation categories related to S_3 and S_4, computes their Hopf-Galois extensions, and shows they are cocycle deformations of graded versions.

Contribution

It provides a complete classification of module categories over these Hopf algebras and analyzes their deformation and extension properties.

Findings

Classified all indecomposable module categories over the specified Hopf algebras.

Computed all Hopf-Galois extensions for these algebras.

Established that these Hopf algebras are cocycle deformations of graded versions.

Abstract

We classify exact indecomposable module categories over the representation category of all non-trivial Hopf algebras with coradical S_3 and S_4. As a byproduct, we compute all its Hopf-Galois extensions and we show that these Hopf algebras are cocycle deformations of their graded versions.