{"paper":{"title":"On homomorphisms from Ringel-Hall algebras to quantum cluster algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Fan Xu, Ming Ding, Xueqing Chen","submitted_at":"2014-02-18T02:52:11Z","abstract_excerpt":"In \\cite{rupel3},the authors defined algebra homomorphisms from the dual Ringel-Hall algebra of certain hereditary abelian category $\\mathcal{A}$ to an appropriate $q$-polynomial algebra. In the case that $\\mathcal{A}$ is the representation category of an acyclic quiver, we give an alternative proof by using the cluster multiplication formulas in \\cite{DX}. Moreover, if the underlying graph of $Q$ is bipartite and the matrix $B$ associated to the quiver $Q$ is of full rank, we show that the image of the algebra homomorphisms is in the corresponding quantum cluster algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4213","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"}