Dual constructions for partial actions of Hopf algebras

The duality between partial actions (partial H-module algebras) and co-actions (partial H-comodule algebras) of a Hopf algebra H is fully explored in this work. A connection between partial (co)actions and Hopf algebroids is established under certain commutativity conditions. Moreover, we continue this duality study, introducing also partial H-module coalgebras and their associated C-rings, partial H-comodule coalgebras and their associated cosmash coproducts, as well as the mutual interrelations between these structures.