{"paper":{"title":"Symmetric bilinear form on a Lie algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Eun-Hee Cho, Sei-Qwon Oh","submitted_at":"2016-05-20T04:58:02Z","abstract_excerpt":"Let $\\frak g$ be the finite dimensional simple Lie algebra associated to an indecomposable and symmetrizable generalized Cartan matrix $C=(a_{ij})_{n\\times n}$ of finite type and let $\\frak d$ be a finite dimensional Lie algebra related to a quantum group $D_{q,p^{-1}}(\\frak g)$ obtained by Hodges, Levasseur and Toro \\cite{HoLeT} by deforming the quantum group $U_q(\\frak g)$.\n  Here we see that $\\frak d$ is a generalization of $\\frak g$ and give a $\\frak d$-invariant symmetric bilinear form on $\\frak d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06214","kind":"arxiv","version":1},"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"}