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arXiv · 2401.15601

On $F$-Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula

Changjian Fu·Liangang Peng·Huihui Ye
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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.

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Changjian Fu, Liangang Peng, Huihui Ye. 2024-01-28. On $F$-Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula. https://doi.org/10.3842/sigma.2024.080

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