A note on a cluster structure of the coordinate ring of a simple algebraic group
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911558982959104 |
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| author | Oya, Hironori |
| author_facet | Oya, Hironori |
| contents | We show that the coordinate ring of a simply-connected simple algebraic group $G$ over the complex number field coincides with the Berenstein--Fomin--Zelevinsky cluster algebra and its upper cluster algebra, at least when $G$ is not of type $F_4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09011 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on a cluster structure of the coordinate ring of a simple algebraic group Oya, Hironori Representation Theory Rings and Algebras 13F60, 20G07, 17B10 We show that the coordinate ring of a simply-connected simple algebraic group $G$ over the complex number field coincides with the Berenstein--Fomin--Zelevinsky cluster algebra and its upper cluster algebra, at least when $G$ is not of type $F_4$. |
| title | A note on a cluster structure of the coordinate ring of a simple algebraic group |
| topic | Representation Theory Rings and Algebras 13F60, 20G07, 17B10 |
| url | https://arxiv.org/abs/2504.09011 |