On Terwilliger $\mathbb{F}$-algebras of factorial association schemes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915580099952640 |
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| author | He, Jiu-Yang Jiang, Yu |
| author_facet | He, Jiu-Yang Jiang, Yu |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_23593 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Terwilliger $\mathbb{F}$-algebras of factorial association schemes He, Jiu-Yang Jiang, Yu Combinatorics Representation Theory 05E30, 05E16 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. |
| title | On Terwilliger $\mathbb{F}$-algebras of factorial association schemes |
| topic | Combinatorics Representation Theory 05E30, 05E16 |
| url | https://arxiv.org/abs/2510.23593 |