On the properties of acyclic sign-skew-symmetric cluster algebras

2023/05/01 by Siyang Liu, Liu, Siyang
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2305.00634

openalex publication_date 2023/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the tropical dualities and properties of exchange graphs for the totally sign-skew-symmetric cluster algebra under a condition. We prove that the condition always holds for acyclic cluster algebras, then all results hold for the acyclic case.

Related

• A short proof for the acyclicity of oriented exchange graphs of cluster algebras
• Categorification of sign-skew-symmetric cluster algebras and some conjectures on g-vectors
• Sign-coherence and tropical sign pattern for rank 3 real cluster-cyclic exchange matrices
• F-invariant in cluster algebras
• Cluster algebras and symmetric matrices