Classifying partial (co)actions of Taft and Nichols Hopf algebras on their base fields

TL;DR

This paper classifies all partial actions and coactions of Taft and Nichols Hopf algebras on their base fields, showing that all such partial (co)actions are symmetric, thereby advancing understanding of their algebraic structure.

Contribution

It provides a complete classification of partial (co)actions of specific Hopf algebras on base fields and proves their symmetry, a novel result in the field.

Findings

All partial actions and coactions are classified.

All partial (co)actions are symmetric.

The classification applies specifically to Taft and Nichols Hopf algebras.

Abstract

In this paper we determine all partial actions and partial coactions of Taft and Nichols Hopf algebras on their base fields. Furthermore, we prove that all such partial (co)actions are symmetric.