Atomic basis of quantum cluster algebra of type \widetildeA_2n-1,1

2020/11/14 by Ming Ding, Fan Xu, Ding, Ming +3
Mathematics · Physics and Astronomy · #16G20 (Primary) 13F60 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2011.07350

openalex publication_date 2020/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Q be the affine quiver of type \widetildeA_2n-1,1 and A_q(Q) be the quantum cluster algebra associated to the valued quiver (Q,(2,2,…,2)). We prove some cluster multiplication formulas, and deduce that the cluster variables associated with vertices of Q satisfy a quantum analogue of the constant coefficient linear relations. We then construct two bar-invariant ℤ[q^±(1)/(2)]-bases B and S of A_q(Q) consisting of positive elements, and prove that B is an atomic basis.

Citations

• Positivity in skew-symmetric cluster algebras of finite type

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