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From quantum groups to quantum cluster algebras (2511.14240v1)
Published 18 Nov 2025 in math.QA, math.RA, and math.RT
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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