PreprintCC BY 4.0arXiv
Quantum cluster structures on bosonic extensions
Abstract
We construct a quantum cluster algebra structure on the standard ℤ[q±1/2]-form of the bosonic extension algebra Â(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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BibTeX
@misc{bi2026quantum,
title = {{Quantum cluster structures on bosonic extensions}},
author = {Yingjin Bi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40058},
eprint = {2610.40058},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40058},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum cluster structures on bosonic extensions
AU - Yingjin Bi
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40058
UR - https://arxiv.org/abs/2610.40058
AB - We construct a quantum cluster algebra structure on the standard ℤ[q^±1/2]-form of the bosonic extension algebra Â(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.
ER -