{"paper":{"title":"Hall algebra approach to Drinfeld's presentation of quantum loop algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Jie Xiao, Rujing Dou, Yong Jiang","submitted_at":"2010-02-05T21:17:28Z","abstract_excerpt":"The quantum loop algebra $U_{v}(\\mathcal{L}\\mathfrak{g})$ was defined as a generalization of the Drinfeld's new realization of the quantum affine algebra to the loop algebra of any Kac-Moody algebra $\\mathfrak{g}$. It has been shown by Schiffmann that the Hall algebra of the category of coherent sheaves on a weighted projective line is closely related to the quantum loop algebra $U_{v}(\\mathcal{L}\\mathfrak{g})$, for some $\\mathfrak{g}$ with a star-shaped Dynkin diagram. In this paper we study Drinfeld's presentation of $U_{v}(\\mathcal{L}\\mathfrak{g})$ in the double Hall algebra setting, based "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.1316","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"}