{"paper":{"title":"Hall algebras and quantum groups associated to Dynkin quivers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Limeng Xia, Yun Gao","submitted_at":"2016-05-01T11:56:23Z","abstract_excerpt":"For Dynkin quivers, we find the Laurent polynomials $\\widetilde{X}_{a, c}^{b}(v)$ and use $\\widetilde{X}_{a, c}^{b}(v)$ to construct the Hall algebra $\\hc_v(\\cc(\\cp))$ over $\\mz[v, v^{-1}]$, where $\\widetilde{X}_{a, c}^{b}(|\\mf_q|)$'s are structure constants used by Bridgeland. The Laurent polynomials $\\widetilde{X}_{a, c}^{b}(v)$ are explicitly given in $A_1$ case. As an application, we obtain the full quantum groups $U_t(\\sg)$ associated to the Dynkin quivers for arbitrary $t\\not=0,\\pm1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00242","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"}