{"paper":{"title":"Structures of Nichols (braided) Lie algebras of diagonal type","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Jing Wang, Shouchuan Zhang, Weicai Wu, Yao-Zhong Zhang","submitted_at":"2017-04-22T15:19:10Z","abstract_excerpt":"Let $V$ be a braided vector space of diagonal type. Let $\\mathfrak B(V)$, $\\mathfrak L^-(V)$ and $\\mathfrak L(V)$ be the Nichols algebra, Nichols Lie algebra and Nichols braided Lie algebra over $V$, respectively. We show that a monomial belongs to $\\mathfrak L(V)$ if and only if that this monomial is connected. We obtain the basis for $\\mathfrak L(V)$ of arithmetic root systems and the dimension for $\\mathfrak L(V)$ of finite Cartan type. We give the sufficient and necessary conditions for $\\mathfrak B(V) = F\\oplus \\mathfrak L^-(V)$ and $\\mathfrak L^-(V)= \\mathfrak L(V)$. We obtain an explici"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06810","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"}