On some H-Galois objects which are distinguished by their polynomial H-identities

TL;DR

This paper demonstrates that over a non-semisimple monomial Hopf algebra, Galois objects are uniquely identified by their polynomial H-identities, extending prior results in the field.

Contribution

It extends the classification of Galois objects by polynomial identities to non-semisimple monomial Hopf algebras, broadening previous understanding.

Findings

Galois objects are distinguished by polynomial H-identities

Extension of Kassel's result to non-semisimple cases

Classification of Galois objects via polynomial identities

Abstract

When k is an algebraically closed field of characteristic 0 and H is a non-semisimple monomial Hopf algebra, we show that all Galois objects over H are determined up to H-comodule algebra isomorphism by their polynomial H-identities, extending a previous result by Kassel.