{"paper":{"title":"Unistructurality of cluster algebras of type ${\\widetilde{\\mathbb{A}}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"V\\'eronique Bazier-Matte","submitted_at":"2015-11-24T17:31:31Z","abstract_excerpt":"It is conjectured by Ibrahim Assem, Ralf Schiffler and Vasilisa Shramchenko in \"Cluster Automorphisms and Compatibility of Cluster Variables\" that every cluster algebra is unistructural, that is to say, that the set of cluster variables determines uniquely the cluster algebra structure. In other words, there exists a unique decomposition of the set of cluster variables into clusters. This conjecture has been proven to hold true for algebras of type Dynkin or rank 2 by Assem, Schiffler and Shramchenko. The aim of this paper is to prove it for algebras of type ${\\widetilde{\\mathbb{A}}}$. We use "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07817","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"}