A short proof for the acyclicity of oriented exchange graphs of cluster algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915241374253056 |
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| author | Deng, Shuhao Fu, Changjian |
| author_facet | Deng, Shuhao Fu, Changjian |
| contents | The statement in the title was proved in \cite{Cao23} 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10245 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A short proof for the acyclicity of oriented exchange graphs of cluster algebras Deng, Shuhao Fu, Changjian Representation Theory Rings and Algebras The statement in the title was proved in \cite{Cao23} 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. |
| title | A short proof for the acyclicity of oriented exchange graphs of cluster algebras |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2504.10245 |