Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras

TL;DR

This paper introduces polynomial identities for comodule algebras over Hopf algebras and demonstrates their effectiveness in classifying Galois objects over specific Hopf algebras.

Contribution

It defines polynomial H-identities for comodule algebras and provides finite sets of identities that distinguish Galois objects over certain Hopf algebras.

Findings

Finite sets of polynomial identities distinguish Galois objects over Taft algebra and E(n).

General properties of polynomial H-identities and T-ideals are established.

Method applicable to classify Galois objects over specific finite-dimensional Hopf algebras.

Abstract

We define polynomial H-identities for comodule algebras over a Hopf algebra H and establish general properties for the corresponding T-ideals. In the case H is a Taft algebra or the Hopf algebra E(n), we exhibit a finite set of polynomial H-identities which distinguish the Galois objects over H up to isomorphism.