Sweedler duality for Hom-(co)algebras and Hom-(co)modules

TL;DR

This paper develops a duality framework for infinite-dimensional Hom-(co)algebras and Hom-(co)modules using Sweedler duality, enabling new morphism constructions and applications to recursive sequences and minimal polynomials.

Contribution

It introduces a duality construction for infinite-dimensional Hom-(co)algebras and Hom-modules, expanding the theoretical toolkit for Hom-algebra structures.

Findings

Established a duality for infinite-dimensional Hom-algebras and Hom-modules.

Derived morphisms between Hom-(co)algebras and Hom-(co)modules under this duality.

Applied the duality to analyze Hom-type recursive sequences and minimal polynomials.

Abstract

We establish a dual version of infinite-dimensional Hom-algebras and Hom-modules by using the Sweedler duality construction. Additionally, linear morphisms between infinite-dimensional Hom-algebras (resp. Hom-modules) and Hom-coalgebras (resp. Hom-comodules) are derived under this construction. As an application, we present a Hom-type binary linearly recursive sequence and show that the Sweedler duality construction can be utilized to determine the minimal polynomials of finite-codimensional ideals.