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A short proof for the acyclicity of oriented exchange graphs of cluster algebras

2025/04/14 by Changjian Fu, Deng, Shuhao, Fu, Changjian
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2504.10245

Abstract

The statement in the title was proved in \citeCao23 by introducing dominant sets of seeds, which are analogs of torsion classes in representation theory. In this note, we observe a short proof by the existence of consistent cluster scattering diagrams.

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