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Positivity for quantum cluster algebras from orbifolds

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arxiv 2406.03362 v1 pith:MUZQC3CV submitted 2024-06-05 math.RA math.COmath.QAmath.RT

Positivity for quantum cluster algebras from orbifolds

classification math.RA math.COmath.QAmath.RT
keywords quantumclustermathcalalgebraarbitrarypositivityalgebrascoefficients
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Let $(S,M,U)$ be a marked orbifold with or without punctures and let $\mathcal A_v$ be a quantum cluster algebra from $(S,M,U)$ with arbitrary coefficients and quantization. We provide combinatorial formulas for quantum Laurent expansion of quantum cluster variables of $\mathcal A_v$ concerning an arbitrary quantum seed. Consequently, the positivity for the quantum cluster algebra $\mathcal A_v$ is proved.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Quantum cluster algebra realization for stated ${\rm SL}_n$-skein algebras and rotation-invariant bases for polygons

    math.QA 2026-05 unverdicted novelty 6.0

    For polygonal surfaces, the localized stated SL_n-skein algebra equals the associated quantum cluster algebra, producing a rotation-invariant basis.