Combinatorics of graded module categories over skew polynomial algebras at roots of unity
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909526273294336 |
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| author | Higashitani, Akihiro Ueyama, Kenta |
| author_facet | Higashitani, Akihiro Ueyama, Kenta |
| contents | We introduce an operation on skew-symmetric matrices over $\mathbb{Z}/\ell\mathbb{Z}$ called switching, and also define a class of skew-symmetric matrices over $\mathbb{Z}/\ell\mathbb{Z}$ referred to as modular Eulerian matrices. We then show that these are closely related to the graded module categories over skew polynomial algebras at $\ell$-th roots of unity. As an application, we study the point simplicial complexes of skew polynomial algebras at cube roots of unity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10904 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Combinatorics of graded module categories over skew polynomial algebras at roots of unity Higashitani, Akihiro Ueyama, Kenta Rings and Algebras Combinatorics Representation Theory We introduce an operation on skew-symmetric matrices over $\mathbb{Z}/\ell\mathbb{Z}$ called switching, and also define a class of skew-symmetric matrices over $\mathbb{Z}/\ell\mathbb{Z}$ referred to as modular Eulerian matrices. We then show that these are closely related to the graded module categories over skew polynomial algebras at $\ell$-th roots of unity. As an application, we study the point simplicial complexes of skew polynomial algebras at cube roots of unity. |
| title | Combinatorics of graded module categories over skew polynomial algebras at roots of unity |
| topic | Rings and Algebras Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2409.10904 |