The Monoidal Hom–Hopf Algebra Arising From Partial Hom-Actions

In this paper, we mainly focus on how to use Hom-partial actions to construct a new monoidal Hom–Hopf algebra. For this, we first introduce the notions of partial Hom–Smash products and partial Hom–Smash coproducts. Then, partial matched Hom-pairs are established to construct monoidal Hom–Hopf algebras, as application, some concrete examples are elaborated.