Fundamental relations in quantum cluster algebras
Junyuan Huang, Xueqing Chen, Ming Ding, Fan Xu
Published: 2025/9/15
Abstract
Let $\mathcal{A}_{q}$ be an arbitrary quantum cluster algebra with principal coefficients. We give the fundamental relations between the quantum cluster variables arising from one-step mutations from the initial cluster in $\mathcal{A}_{q}$. Immediately and directly, we obtain an algebra homomorphism from the corresponding (untwisted) quantum group to $\mathcal{A}_{q}$.