{"paper":{"title":"Local Lie derivations on von Neumann algebras and algebras of locally measurable operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Guangyu An, Jun He","submitted_at":"2018-06-07T14:11:51Z","abstract_excerpt":"Let $\\mathcal{A}$ be a unital associative algebra and $\\mathcal{M}$ be an $\\mathcal{A}$-bimodule. A linear mapping $\\varphi$ from $\\mathcal{A}$ into an $\\mathcal{A}$-bimodule $\\mathcal{M}$ is called a Lie derivation if $\\varphi[A,B]=[\\varphi(A),B]+[A,\\varphi(B)]$ for each $A,B$ in $\\mathcal{A}$, and $\\varphi$ is called a \\emph{local Lie derivation} if for every $A$ in $\\mathcal{A}$, there exists a Lie derivation $\\varphi_{A}$ (depending on $A$) from $\\mathcal{A}$ into $\\mathcal{M}$ such that $\\varphi(A)=\\varphi_{A}(A)$. In this paper, we prove that every local Lie derivation on von Neumann alg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03189","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"}