English

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

Rings and Algebras 2024-09-04 v3 Quantum Algebra

Abstract

We show the polynomial property of FF-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 FF-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

Cite

@article{arxiv.2401.15601,
  title  = {On $F$-Polynomials for Generalized Quantum Cluster Algebras and Gupta's Formula},
  author = {Changjian Fu and Liangang Peng and Huihui Ye},
  journal= {arXiv preprint arXiv:2401.15601},
  year   = {2024}
}