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arXiv · 2405.11838

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

Jiacheng Sun·Shuanhong Wang·Chi Zhang·Haoran Zhu
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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.

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Jiacheng Sun, Shuanhong Wang, Chi Zhang, Haoran Zhu. 2024-05-20. Sweedler duality for Hom-(co)algebras and Hom-(co)modules. https://doi.org/10.1007/s44198-025-00310-8

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