From quantum groups to quantum cluster algebras

2025/11/18 by Fu, Changjian, Zhang, Haicheng
Mathematics · #Algebraic structures and combinatorial models #Advanced Operator Algebra Research #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2511.14240

Abstract

We provide a homomorphism of algebras from the quantum group U⁺_v(\mathfrakg) to the corresponding quantum cluster algebra \mathcal A_q with principal coefficients. As a by-product, we show that the quantum cluster variables arising from one-step mutations from the initial cluster variables satisfy the (high order) quantum Serre relations in \mathcal A_q.

Related

• Fundamental relations in quantum cluster algebras
• Quantum cluster algebras
• Cluster Nature of Quantum Groups
• Integral quantum cluster structures
• Quantum cluster variables via canonical submodules