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From the quantum group Uq1/2( sl̂2 ) to the Kronecker quantum cluster algebra
Abstract
Let 𝒜q be the Kronecker quantum cluster algebra with principal coefficients. We construct an explicit algebra homomorphism from the whole quantum group Uq1/2( sl2̂ ) to 𝒜q, whose images together with either of the two frozen variables generate 𝒜q. As an application, we obtain algebra homomorphisms from the split imathquantum groups of affine sl̂2 to 𝒜q. Moreover, we explicitly determine the images of the positive and negative real and imaginary root vectors of Uq1/2( sl2̂ ) in terms of quantum cluster variables.
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BibTeX
@misc{huang2026from,
title = {{From the quantum group $U_q^1/2( \widehat \mathfraksl_2 )$ to the Kronecker quantum cluster algebra}},
author = {Junyuan Huang and Xueqing Chen and Ming Ding and Fan Xu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06256},
eprint = {2611.06256},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06256},
}
RIS
TY - UNPB
TI - From the quantum group U_q^1/2( sl̂_2 ) to the Kronecker quantum cluster algebra
AU - Junyuan Huang
AU - Xueqing Chen
AU - Ming Ding
AU - Fan Xu
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06256
UR - https://arxiv.org/abs/2611.06256
AB - Let 𝒜_q be the Kronecker quantum cluster algebra with principal coefficients. We construct an explicit algebra homomorphism from the whole quantum group U_q^1/2( sl_2̂ ) to 𝒜_q, whose images together with either of the two frozen variables generate 𝒜_q. As an application, we obtain algebra homomorphisms from the split imathquantum groups of affine sl̂_2 to 𝒜_q. Moreover, we explicitly determine the images of the positive and negative real and imaginary root vectors of U_q^1/2( sl_2̂ ) in terms of quantum cluster variables.
ER -