Quantum cluster structures on bosonic extensions

Yingjin Bi

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arXiv · 2610.40058

Quantum cluster structures on bosonic extensions

Yingjin Bi

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Abstract

We construct a quantum cluster algebra structure on the standard $\mathbb Z[q^{\pm1/2}]$-form of the bosonic extension algebra $\widehat A(b)$ for every positive braid $b$ and every symmetrizable generalized Cartan matrix. The proof realizes this algebra as the degree-zero part of a localization of a larger quantum unipotent coordinate ring, obtained by thickening a word for $b$. For symmetric Cartan matrices, this realization also gives a monoidal categorification of the quantum cluster algebra.

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Yingjin Bi. 2026-10-29. Quantum cluster structures on bosonic extensions. https://arxiv.org/abs/2610.40058

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