On the acyclic quantum cluster algebras with principal coefficients

2024/07/25 by Junyuan Huang, Huang, Junyuan, Xueqing Chen +5
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2407.17685

openalex publication_date 2024/07/25 · openalex created_date 2024/09/19 · openalex updated_date 2026/07/28

Abstract

In this paper, we focus on a new lower bound quantum cluster algebra which is generated by the initial quantum cluster variables and the quantum projective cluster variables of an acyclic quantum cluster algebra with principal coefficients. We show that the new lower bound quantum cluster algebra coincides with the corresponding acyclic quantum cluster algebra. Moreover, we establish a class of formulas between these generators, and obtain the dual PBW basis of this algebra.

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