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arXiv · 2509.11635

Fundamental relations in quantum cluster algebras

Junyuan Huang·Xueqing Chen·Ming Ding·Fan Xu
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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 $\mathcal{A}_{q}$.

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Junyuan Huang, Xueqing Chen, Ming Ding, Fan Xu. 2025-09-15. Fundamental relations in quantum cluster algebras. https://arxiv.org/abs/2509.11635

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