{"paper":{"title":"Multiplicative properties of a quantum Caldero-Chapoton map associated to valued quivers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Jie Sheng, Ming Ding","submitted_at":"2011-09-25T10:04:23Z","abstract_excerpt":"We prove a multiplication theorem of a quantum Caldero-Chapoton map associated to valued quivers which extends the results in \\cite{DX}\\cite{D}. As an application, when $Q$ is a valued quiver of finite type or rank 2, we obtain that the algebra $\\mathcal{AH}_{|k|}(Q)$ generated by all cluster characters (see Definition \\ref{def}) is exactly the quantum cluster algebra $\\mathcal{EH}_{|k|}(Q)$ and various bases of the quantum cluster algebras of rank 2 can naturally be deduced."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5342","kind":"arxiv","version":1},"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"}