English

Fundamental relations in quantum cluster algebras

Quantum Algebra 2025-09-16 v1 Representation Theory

Abstract

Let Aq\mathcal{A}_{q} be an arbitrary quantum cluster algebra with principal coefficients. We give the fundamental relations between the quantum cluster variables arising from one-step mutations from the initial cluster in Aq\mathcal{A}_{q}. Immediately and directly, we obtain an algebra homomorphism from the corresponding (untwisted) quantum group to Aq\mathcal{A}_{q}.

Keywords

Cite

@article{arxiv.2509.11635,
  title  = {Fundamental relations in quantum cluster algebras},
  author = {Junyuan Huang and Xueqing Chen and Ming Ding and Fan Xu},
  journal= {arXiv preprint arXiv:2509.11635},
  year   = {2025}
}
R2 v1 2026-07-01T05:36:17.295Z