{"paper":{"title":"Local automorphisms of finite dimensional simple Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Mauro Costantini","submitted_at":"2018-05-29T10:05:50Z","abstract_excerpt":"Let ${\\mathfrak g}$ be a finite dimensional simple Lie algebra over an algebraically closed field $K$ of characteristic $0$. A linear map $\\varphi:{\\mathfrak g}\\to {\\mathfrak g}$ is called a local automorphism if for every $x$ in ${\\mathfrak g}$ there is an automorphism $\\varphi_x$ of ${\\mathfrak g}$ such that $\\varphi(x)=\\varphi_x(x)$. We prove that a linear map $\\varphi:{\\mathfrak g}\\to {\\mathfrak g}$ is local automorphism if and only if it is an automorphism or an anti-automorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11338","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"}