Work

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

Year: 2024

Type: article

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.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2024.080

Authors: Changjian Fu, Liangang Peng, Huihui Ye

Institution: Sichuan University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Natural Science Foundation of China

Award: G4553424203