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math.QA — Quantum Algebra

Strongly positive bases in rank-two quantum cluster algebras

Contributed by 琪越唐

We prove Conjecture 12 of Lee, Li, Rupel, and Zelevinsky: for arbitrary positive integers $b,c$ , every strongly positive basis of the coefficient-free rank-two quantum cluster algebra $\mathcal A_v(b,c)$ contains a unique element pointed at each pair in $\mathbb Z^2$ . These pointed elements exhaust the basis.

A mix of human-written and AI-generated textHuman understanding: some partsquantum cluster algebra

Sep 30, 2026PDF ↗View work →

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