On $F$-Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula
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Published:2024-09-03
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ISSN:1815-0659
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Container-title:Symmetry, Integrability and Geometry: Methods and Applications
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Short-container-title:SIGMA
Author:
,Fu Changjian,Peng Liangang, ,Ye Huihui,
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.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)