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arXiv · 2510.17216

Radford $[(m,k),m]$-biproduct Theorem for Generalized Hom-crossed Products

Botong Gai·Shuanhong Wang
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Abstract

In this paper, we mainly provide a new approache to construct Hom-Hopf algebras. For this, we introduce and study the notion of a left $(m,k)$-Hom-crossed product structure as a generalization of $k$-Hom-smash product structure. Then one combines this $(m,k)$-Hom-crossed product structure and a left $m$-Hom-smash coproduct structure to build Radford $[(m,k),m]$-biproduct theorem. Finally, we study Hom admissible mappping system to characterize this Radford $[(m,k),m]$-biproduct structure.

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Botong Gai, Shuanhong Wang. 2025-10-20. Radford $[(m,k),m]$-biproduct Theorem for Generalized Hom-crossed Products. https://arxiv.org/abs/2510.17216

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