{"paper":{"title":"Quasi-homomorphisms of quantum cluster algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Jian-Rong Li, Min Huang, Wen Chang","submitted_at":"2023-03-23T04:29:50Z","abstract_excerpt":"In this paper, we study quasi-homomorphisms of quantum cluster algebras, which are quantum analogy of quasi-homomorphisms of cluster algebras introduced by Fraser.\n  For a quantum Grassmannian cluster algebra $\\mathbb{C}_q[{\\rm Gr}(k,n)]$, we show that there is an associated braid group and each generator $\\sigma_i$ of the braid group preserves the quasi-commutative relations of quantum Pl\\\"{u}cker coordinates and exchange relations of the quantum Grassmannian cluster algebra. We conjecture that $\\sigma_i$ also preserves $r$-term ($r \\ge 4$) quantum Pl\\\"{u}cker relations of $\\mathbb{C}_q[{\\rm "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.13030","kind":"arxiv","version":3},"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/2303.13030/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"}