Structure of Terwilliger algebras of quasi-thin association schemes
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916457348071424 |
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| author | Chen, Zhenxian Xi, Changchang |
| author_facet | Chen, Zhenxian Xi, Changchang |
| contents | We show that the Terwilliger algebra of a quasi-thin association scheme over a field is always a quasi-hereditary cellular algebra in the sense of Cline-Parshall-Scott and of Graham-Lehrer, repsectively, and that the basic algebra of the Terwilliger algebra is the dual extension of a star with all arrows pointing to its center if the field has characteristic $2$. Thus many homological and representation-theoretic properties of these Terwilliger algebras can be determined completely. For example, the Nakayama conjecture holds for Terwilliger algebras of quasi-thin association schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21600 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Structure of Terwilliger algebras of quasi-thin association schemes Chen, Zhenxian Xi, Changchang Combinatorics Rings and Algebras Representation Theory Primary 05E30, 16G10, 15A30, Secondary 16S10, 05E16 We show that the Terwilliger algebra of a quasi-thin association scheme over a field is always a quasi-hereditary cellular algebra in the sense of Cline-Parshall-Scott and of Graham-Lehrer, repsectively, and that the basic algebra of the Terwilliger algebra is the dual extension of a star with all arrows pointing to its center if the field has characteristic $2$. Thus many homological and representation-theoretic properties of these Terwilliger algebras can be determined completely. For example, the Nakayama conjecture holds for Terwilliger algebras of quasi-thin association schemes. |
| title | Structure of Terwilliger algebras of quasi-thin association schemes |
| topic | Combinatorics Rings and Algebras Representation Theory Primary 05E30, 16G10, 15A30, Secondary 16S10, 05E16 |
| url | https://arxiv.org/abs/2410.21600 |