{"paper":{"title":"Gr\\\"obner-Shirshov bases for some Lie algebras","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Qingyan Tang, Yu Li, Yuqun Chen","submitted_at":"2013-05-15T23:37:59Z","abstract_excerpt":"We give Gr\\\"obner-Shirshov bases for Drinfeld-Kohno Lie algebra $\\textbf{L}_{n}$ in \\cite{[Et]} and Kukin Lie algebra $A_P$ in \\cite{Kukin}, where $P$ is a semigroup. As applications, we show that as $\\mathbb{Z}$-module $\\textbf{L}_{n}$ is free and a $\\mathbb{Z}$-basis of $\\textbf{L}_{n}$ is given. We give another proof of Kukin Theorem: if semigroup $P$ has the undecidable word problem then the Lie algebra $A_P$ has the same property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4546","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"}