On -Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula
We show the polynomial property of -polynomials for generalized quantum cluster algebras and obtain the associated separation formulas under a mild condition. Along the way, we obtain Gupta's formulas of -polynomials for generalized quantum cluster algebras. These formulas specialize to Gupta&#...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212340 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On -Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula. Changjian Fu, Liangang Peng and Huihui Ye. SIGMA 20 (2024), 080, 26 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862726317687963648 |
|---|---|
| author | Fu, Changjian Peng, Liangang Ye, Huihui |
| author_facet | Fu, Changjian Peng, Liangang Ye, Huihui |
| citation_txt | On -Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula. Changjian Fu, Liangang Peng and Huihui Ye. SIGMA 20 (2024), 080, 26 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We show the polynomial property of -polynomials for generalized quantum cluster algebras and obtain the associated separation formulas under a mild condition. Along the way, we obtain Gupta's formulas of -polynomials for generalized quantum cluster algebras. These formulas specialize to Gupta's formulas for quantum cluster algebras and cluster algebras, respectively. Finally, a generalization of Gupta's formula has also been discussed in the setting of generalized cluster algebras.
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| first_indexed | 2026-03-21T09:25:29Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212340 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T09:25:29Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Fu, Changjian Peng, Liangang Ye, Huihui 2026-02-05T09:53:24Z 2024 On -Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula. Changjian Fu, Liangang Peng and Huihui Ye. SIGMA 20 (2024), 080, 26 pages 1815-0659 2020 Mathematics Subject Classification: 13F60; 16S34; 05E16 arXiv:2401.15601 https://nasplib.isofts.kiev.ua/handle/123456789/212340 https://doi.org/10.3842/SIGMA.2024.080 We show the polynomial property of -polynomials for generalized quantum cluster algebras and obtain the associated separation formulas under a mild condition. Along the way, we obtain Gupta's formulas of -polynomials for generalized quantum cluster algebras. These formulas specialize to Gupta's formulas for quantum cluster algebras and cluster algebras, respectively. Finally, a generalization of Gupta's formula has also been discussed in the setting of generalized cluster algebras. The authors are grateful to Professor Xueqing Chen for helpful comments. The authors thank the referees for their valuable comments and suggestions in making this article more readable. This work is partially supported by the National Natural Science Foundation of China (Grant No. 11971326). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On -Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula Article published earlier |
| spellingShingle | On -Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula Fu, Changjian Peng, Liangang Ye, Huihui |
| title | On -Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula |
| title_full | On -Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula |
| title_fullStr | On -Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula |
| title_full_unstemmed | On -Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula |
| title_short | On -Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula |
| title_sort | on -polynomials for generalized quantum cluster algebras and gupta's formula |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212340 |
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