Twisted partial actions of Hopf algebras

TL;DR

This paper introduces the concept of twisted partial Hopf actions, unifying various partial actions of groups and Hopf algebras, and explores their algebraic structures and examples.

Contribution

It defines twisted partial Hopf actions, establishes conditions for partial cocycles, and connects these to partial crossed products and algebra extensions.

Findings

Defined twisted partial Hopf actions

Established conditions for partial cocycles

Connected partial actions to algebra extensions

Abstract

In this work, the notion of a twisted partial Hopf action is introduced as a unified approach for twisted partial group actions, partial Hopf actions and twisted actions of Hopf algebras. The conditions on partial cocycles are established in order to construct partial crossed products, which are also related to partially cleft extensions of algebras. Examples are elaborated using algebraic groups.