On $F$-Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914932870610944 |
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| author | Fu, Changjian Peng, Liangang Ye, Huihui |
| author_facet | Fu, Changjian Peng, Liangang Ye, Huihui |
| contents | We show the polynomial property of $F$-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 $F$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15601 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On $F$-Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula Fu, Changjian Peng, Liangang Ye, Huihui Rings and Algebras Quantum Algebra We show the polynomial property of $F$-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 $F$-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. |
| title | On $F$-Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula |
| topic | Rings and Algebras Quantum Algebra |
| url | https://arxiv.org/abs/2401.15601 |