{"paper":{"title":"Finiteness of Nichols Algebras and Nichols (Braided) Lie Algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Shouchuan Zhang, Weicai Wu, Yao-Zhong Zhang","submitted_at":"2016-07-27T04:44:44Z","abstract_excerpt":"It is shown that if $\\mathfrak B(V) $ is connected Nichols algebra of diagonal type with $\\dim V>1$, then $\\dim (\\mathfrak L^-(V)) = \\infty$ $($resp. $ \\dim (\\mathfrak L(V)) = \\infty $$)$ $($ resp. $ \\dim (\\mathfrak B(V)) = \\infty $$)$ if and only if $\\Delta(\\mathfrak B(V)) $ is an arithmetic root system and the quantum numbers (i.e. the fixed parameters) of generalized Dynkin diagrams of $V$ are of finite order. Sufficient and necessary conditions for $m$-fold adjoint action in $\\mathfrak B(V)$ equal to zero, viz. $\\overline{l}_{x_{i}}^{m}[x_{j}]^ -=0$ for $x_i,~x_j\\in \\mathfrak B(V)$, are gi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07955","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"}