From quantum groups to quantum cluster algebras

Changjian Fu; Haicheng Zhang

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arXiv · 2511.14240

From quantum groups to quantum cluster algebras

Changjian Fu·Haicheng Zhang

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Abstract

We provide a homomorphism of algebras from the quantum group $\mathbf{U}^+_v(\mathfrak{g})$ to the corresponding quantum cluster algebra $\mathcal {A}_q$ with principal coefficients. As a by-product, we show that the quantum cluster variables arising from one-step mutations from the initial cluster variables satisfy the (high order) quantum Serre relations in $\mathcal {A}_q$.

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Changjian Fu, Haicheng Zhang. 2025-11-18. From quantum groups to quantum cluster algebras. https://arxiv.org/abs/2511.14240

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