{"paper":{"title":"Cohomological Hall algebras and affine quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Gufang Zhao, Yaping Yang","submitted_at":"2016-04-07T03:52:02Z","abstract_excerpt":"We study the preprojective cohomological Hall algebra (CoHA) introduced by the authors in an earlier work for any quiver $Q$ and any one-parameter formal group $\\mathbb{G}$. In this paper, we construct a comultiplication on the CoHA, making it a bialgebra. We also construct the Drinfeld double of the CoHA. The Drinfeld double is a quantum affine algebra of the Lie algebra $\\mathfrak{g}_Q$ associated to $Q$, whose quantization comes from the formal group $\\mathbb{G}$. We prove, when the group $\\mathbb{G}$ is the additive group, the Drinfeld double of the CoHA is isomorphic to the Yangian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01865","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"}