{"paper":{"title":"Isomorphisms and automorphisms of quantum groups","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Jie-Tai Yu, Li-Bin Li","submitted_at":"2009-10-09T11:35:06Z","abstract_excerpt":"We consider isomorphisms and automorphisms of quantum groups. Let $k$ be a field and suppose $p, q\\in k^*$ are not roots of unity. We prove that the two quantum groups $U_q(\\mathfrak {sl}_2)$ and $U_p(\\mathfrak{sl}_2)$ over a field $k$ are isomorphic as $k$-algebras if and only if $p=q^{\\pm 1}$. We also rediscover the description of the group of all $k$-automorphisms of $U_q(\\mathfrak{sl}_2)$ of Alev and Chamarie, and that $\\text{Aut}_k(U_q(\\mathfrak {sl}_2))$ is isomorphic to $\\text{Aut}_k(U_p(\\mathfrak {sl}_2))$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1713","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"}