Positivity for quantum cluster algebras from orbifolds

Min Huang

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arXiv · 2406.03362

Positivity for quantum cluster algebras from orbifolds

Min Huang

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Abstract

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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Min Huang. 2024-06-05. Positivity for quantum cluster algebras from orbifolds. https://arxiv.org/abs/2406.03362

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