Partial Actions of Weak Hopf Algebras on Coalgebras

TL;DR

This paper introduces and explores the theory of partial actions of weak Hopf algebras and groupoids on coalgebras, establishing equivalences, dualities, and a globalization theorem for these structures.

Contribution

It develops the foundational concepts of partial actions on coalgebras, proves their equivalence with groupoid actions, and establishes a duality with algebra actions, including a globalization result.

Findings

Defined partial actions of weak Hopf algebras on coalgebras

Proved the equivalence between partial actions of groupoids and weak Hopf algebras

Established a duality between partial actions on coalgebras and algebras

Abstract

In this work the notions of partial action of a weak Hopf algebra on a coalgebra and partial action of a groupoid on a coalgebra will be introduced, just as some important properties. An equivalence between these notions will be presented. Finally, a dual relation between the structures of partial action on a coalgebra and partial action on an algebra will be established, as well as a globalization theorem for partial module coalgebras will be presented.