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<p>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 sequences and show that the Sweedler duality construction can be utilized to determine the minimal polynomials of finite-codimensional ideals.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月28日

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  • Jiacheng Sun,
  • Shuanhong Wang,
  • Chi Zhang,
  • Haoran Zhu

摘要

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 sequences and show that the Sweedler duality construction can be utilized to determine the minimal polynomials of finite-codimensional ideals.