{"paper":{"title":"Cluster automorphism groups of cluster algebras of finite type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bin Zhu, Wen Chang","submitted_at":"2015-06-05T15:58:05Z","abstract_excerpt":"We study the cluster automorphism group $Aut(\\mathcal{A})$ of a coefficient free cluster algebra $\\mathcal{A}$ of finite type. A cluster automorphism of $\\mathcal{A}$ is a permutation of the cluster variable set $\\mathscr{X}$ that is compatible with cluster mutations. We show that, on the one hand, by the well-known correspondence between $\\mathscr{X}$ and the almost positive root system $\\Phi_{\\geq -1}$ of the corresponding Dynkin type, the piecewise-linear transformations $\\tau_+$ and $\\tau_-$ on $\\Phi_{\\geq -1}$ induce cluster automorphisms $f_+$ and $f_-$ of $\\mathcal{A}$ respectively; on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01950","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}