{"paper":{"title":"On noncommutative bases of the free module $W_n(\\mathbb K)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ievgen Makedonskyi","submitted_at":"2011-05-24T12:31:52Z","abstract_excerpt":"Let $\\mathbb{K}$ be an algebraically closed field of characteristic zero and $R=\\mathbb{K}[x_1,x_2,...x_n]$ the polynomial ring in $n$ variables over $\\mathbb K.$ We study bases of the free $R$-module $W_n(\\mathbb{K})$ of all $\\mathbb{K}$-derivations of the ring $R$, such that their linear span over $\\mathbb K$ is a subalgebra of the Lie algebra $W_n(\\mathbb{K})$. We proved that for any Lie algebra $L$ of dimension $n$ over $\\mathbb{K}$ there exists a subalgebra $\\bar{L}$ of $W_n(\\mathbb{K})$ which is isomorphic to $L$ and such that every $\\mathbb{K}$-basis of $\\bar L$ is an $R$-basis of the $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4748","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"}