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arXiv · 2510.23593

On Terwilliger $\mathbb{F}$-algebras of factorial association schemes

Jiu-Yang He·Yu Jiang
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Abstract

The Terwilliger algebras of association schemes over an arbitrary field $\mathbb{F}$ were called the Terwilliger $\mathbb{F}$-algebras of association schemes in [9]. In this paper, we study the Terwilliger $\mathbb{F}$-algebras of factorial association schemes. We determine the centers, the semisimplicity, the Jacobson radicals and their nilpotent indices, the Wedderburn-Artin decompositions of the Terwilliger $\mathbb{F}$-algebras of factorial association schemes. Moreover, we determine all Terwilliger $\mathbb{F}$-algebras of factorial association schemes that are the symmetric $\mathbb{F}$-algebras or the Frobenius $\mathbb{F}$-algebras.

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Jiu-Yang He, Yu Jiang. 2025-10-27. On Terwilliger $\mathbb{F}$-algebras of factorial association schemes. https://arxiv.org/abs/2510.23593

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