Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Bi, Yingjin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224911615