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Fundamental relations in quantum cluster algebras (2509.11635v1)
Published 15 Sep 2025 in math.QA and math.RT
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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