{"paper":{"title":"Dual Affine Quantum Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"q-alg","authors_text":"Fabio Gavarini","submitted_at":"1997-12-03T09:55:50Z","abstract_excerpt":"Let $\\hat{\\mathfrak{g}}$ be an untwisted affine Kac-Moody algebra, with its Sklyanin-Drinfel'd structure of Lie bialgebra, and let $\\hat{\\mathfrak{h}}$ be the dual Lie bialgebra. By dualizing the quantum double construction - via formal Hopf algebras - we construct a new quantum group $U_q(\\hat{\\mathfrak{h}})$, dual of $U_q(\\hat{\\mathfrak{g}})$. Studying its restricted and unrestricted integer forms and their specializations at roots of 1 (in particular, their classical limits), we prove that $U_q(\\hat{\\mathfrak{h}})$ yields quantizations of $\\hat{\\mathfrak{h}}$ and $\\hat{G}^\\infty$ (the forma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9712013","kind":"arxiv","version":3},"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"}