{"paper":{"title":"The $ R $--matrix action of untwisted affine quantum groups at roots of 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Fabio Gavarini","submitted_at":"1998-05-04T12:36:33Z","abstract_excerpt":"Let $\\hat{\\frak g}$ be an untwisted affine Kac-Moody algebra. The quantum group $U_h(\\hat{\\frak g})$ (over $\\mathbb{C}[[h]]$) is known to be a quasitriangular Hopf algebra: in particular, it has a universal $ R $--matrix, which yields an $ R $--matrix for each pair of representations of $U_h(\\hat{\\frak g})$. On the other hand, the quantum group $U_q(\\hat{\\frak g})$ (over $\\mathbb{C}(q) $) also has an $ R $--matrix for each pair of representations, but it has not a universal $ R $--matrix so that one cannot say that it is quasitriangular. Following Reshetikin, one introduces the (weaker) notion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9805009","kind":"arxiv","version":4},"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"}