{"paper":{"title":"On the center of the quantized enveloping algebra of a simple Lie algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Libin Li, Limeng Xia, Yinhuo Zhang","submitted_at":"2016-07-04T09:52:09Z","abstract_excerpt":"Let $\\frak{g}$ be a finite dimensional simple complex Lie algebra and $U=U_q(\\frak{g})$ the quantized enveloping algebra (in the sense of Jantzen) with $q$ being generic. In this paper, we show that the center $Z(U_q(\\frak{g}))$ of the quantum group $U_q(\\frak{g})$ is isomorphic to a monoid algebra, and that $Z(U_q(\\frak{g}))$ is a polynomial algebra if and only if $\\frak{g}$ is of type $A_1, B_n, C_n, D_{2k+2}, E_7, E_8, F_4$ or $G_2.$ Moreover, in case $\\frak{g}$ is of type $D_{n}$ with $n$ odd, then $Z(U_q(\\frak{g}))$ is isomorphic to a quotient algebra of a polynomial algebra in $n+1$ vari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00802","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"}