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

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

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 G...

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Veröffentlicht in:Symmetry, integrability and geometry, methods and applications integrability and geometry, methods and applications, 2024-09
Hauptverfasser: Fu, Changjian, Peng, Liangang, Ye, Huihui
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Ye, Huihui
description 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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title On $F$-Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula
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