Reductive monoids and cluster algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866917162184081408 |
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| author | Song, Jinfeng Ye, Jeff York |
| author_facet | Song, Jinfeng Ye, Jeff York |
| contents | We show that the coordinate ring of the Vinberg monoid of a simply connected semisimple complex group is an upper cluster algebra. As an application, we construct cluster structures on a large class of flat reductive monoids. After localization, we obtain cluster structures on any connected reductive group whose commutator group is simply connected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09564 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reductive monoids and cluster algebras Song, Jinfeng Ye, Jeff York Representation Theory Rings and Algebras We show that the coordinate ring of the Vinberg monoid of a simply connected semisimple complex group is an upper cluster algebra. As an application, we construct cluster structures on a large class of flat reductive monoids. After localization, we obtain cluster structures on any connected reductive group whose commutator group is simply connected. |
| title | Reductive monoids and cluster algebras |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2512.09564 |