From quantum groups to quantum cluster algebras
Fuente:
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_ | 1866911273825861632 |
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| author | Fu, Changjian Zhang, Haicheng |
| author_facet | Fu, Changjian Zhang, Haicheng |
| contents | We provide a homomorphism of algebras from the quantum group $\mathbf{U}^+_v(\mathfrak{g})$ to the corresponding quantum cluster algebra $\mathcal {A}_q$ with principal coefficients. As a by-product, we show that the quantum cluster variables arising from one-step mutations from the initial cluster variables satisfy the (high order) quantum Serre relations in $\mathcal {A}_q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14240 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From quantum groups to quantum cluster algebras Fu, Changjian Zhang, Haicheng Quantum Algebra Rings and Algebras Representation Theory We provide a homomorphism of algebras from the quantum group $\mathbf{U}^+_v(\mathfrak{g})$ to the corresponding quantum cluster algebra $\mathcal {A}_q$ with principal coefficients. As a by-product, we show that the quantum cluster variables arising from one-step mutations from the initial cluster variables satisfy the (high order) quantum Serre relations in $\mathcal {A}_q$. |
| title | From quantum groups to quantum cluster algebras |
| topic | Quantum Algebra Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2511.14240 |