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Quantum Algebra

math.QA — Quantum Algebra

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math.QA — Quantum Algebra

The support conjecture for rank-two quantum triangular bases

Contributed by 琪越唐

We prove Conjecture 11 of Lee, Li, Rupel, and Zelevinsky on the support of triangular basis elements in rank-two quantum cluster algebras.

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

Sep 30, 2026PDF ↗View work →

hexagon:2609.00143v1

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 →

hexagon:2609.00124v2

math.QA — Quantum Algebra

Quantum Laurent Positivity for Mutation-Acyclic Cluster Algebras

Contributed by 琪越唐

We prove quantum Laurent positivity for mutation-acyclic skew-symmetrizable cluster algebras of arbitrary finite rank.

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

Sep 29, 2026PDF ↗View work →