{"paper":{"title":"Monoidal categorification of generalized cluster algebras and conjectures of Fraser and Gleitz","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Jian-Rong Li, Xiao-Juan An, Yan-Feng Luo","submitted_at":"2026-06-15T07:56:39Z","abstract_excerpt":"Hernandez and Leclerc introduced the notion of monoidal categorification of cluster algebras. We define similarly the notion of monoidal categorifications of generalized cluster algebras: an abelian monoidal category $\\mathcal M$ is said to be a monoidal categorification of a generalized cluster algebra $\\mathcal A$ if the Grothendieck ring of $\\mathcal M$ is isomorphic to the upper generalized cluster algebra $\\mathcal A^{\\mathrm{up}}$, and if cluster monomials (resp. cluster variables) of $\\mathcal A$ correspond to classes of real simple (resp. real prime simple) objects of $\\mathcal M$.\n  L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.16361","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.16361/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}