Article
| Title: | 2nd-stage quantized cluster algebra on quantum coordinate ring of the special linear group (English) |
| Author: | Sun, Jia |
| Author: | Tang, Xiaomin |
| Author: | Zhang, Yu |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 1 |
| Year: | 2026 |
| Pages: | 47-74 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $\mathbb {C}_q[SL(n+1)]$ denote the quantum coordinate ring of the special linear group which has a quantum cluster structure denoted by $\mathcal {A}_q$. Let $\mathcal {A}_{p,q}$ be the \hbox {2nd-stage} quantization of the quantum cluster algebra $\mathcal {A}_q$, equipped with a compatible Poisson structure $\{-,-\}$. The purpose of this paper is to describe the structure of the 2nd-stage quantized cluster algebra $\mathcal {A}_{p,q}$. We prove that for $n\geq 2$, the 2nd-stage quantized cluster algebra $\mathcal {A}_{p,q}$ is trivial. Additionally, we provide a detailed description of the compatible Poisson structure on $\mathcal {A}_q$. (English) |
| Keyword: | quantum coordinate ring |
| Keyword: | 2nd-stage quantized cluster algebra |
| Keyword: | compatible Poisson structure |
| MSC: | 13F60 |
| MSC: | 17B37 |
| DOI: | 10.21136/CMJ.2026.0108-25 |
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| Date available: | 2026-03-13T09:28:21Z |
| Last updated: | 2026-03-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153560 |
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