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Symmetry, Integrability and Geometry: Methods and Applications, 2024, Volume 20, 080, 26 pp.
DOI: https://doi.org/10.3842/SIGMA.2024.080 (Mi sigma2082) 		 
On $F$-Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula

Changjian Fu, Liangang Peng, Huihui Ye

Department of Mathematics, Sichuan University, Chengdu 610064, P.R. China
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DOI: https://doi.org/10.3842/SIGMA.2024.080
Abstract: 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.
Keywords: $F$-polynomial, separation formula, Fock–Goncharov decomposition, generalized quantum cluster algebra, generalized cluster algebra.
Funding agency Grant number
National Natural Science Foundation of China 11971326
This work is partially supported by the National Natural Science Foundation of China (Grant No. 11971326).
Received: March 12, 2024; in final form August 25, 2024; Published online September 3, 2024
Document Type: Article
MSC: 13F60, 16S34, 05E16
Language: English
Citation: Changjian Fu, Liangang Peng, Huihui Ye, “On $F$-Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula”, SIGMA, 20 (2024), 080, 26 pp.
Citation in format AMSBIB
\Bibitem{FuPenYe24}
\by Changjian~Fu, Liangang~Peng, Huihui~Ye
\paper On $F$-Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula
\jour SIGMA
\yr 2024
\vol 20
\papernumber 080
\totalpages 26
\mathnet{http://mi.mathnet.ru/sigma2082}
\crossref{https://doi.org/10.3842/SIGMA.2024.080}
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