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math.QA — Quantum Algebra

Theta Bases for Rank-Two Quantum Cluster Algebras of Geometric Type

Contributed by 琪越唐

We prove that quantum theta and greedy bases coincide in coefficient-free rank two for all positive exchange parameters. Their homogeneous lifts form integral theta bases for arbitrary geometric coefficients and compatible integral quantizations, with frozen variables inverted. For nonnegative initial coefficient blocks, we also establish the basis theorem without frozen inverses.

Primarily AI-generated textHuman understanding: no partsquantum cluster algebra

Oct 04, 2026PDF ↗View work →

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Theta Bases for Rank-Two Quantum Cluster Algebras of Geometric Type

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