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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1805.11338","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-05-29T10:05:50Z","cross_cats_sorted":[],"title_canon_sha256":"96e9a81c0356a96b49964fe11865be2efa89270d391a1ca2a9a2c3c94ba9168d","abstract_canon_sha256":"70c0135f36ad3187a64ed77d88bc00fbfd6ac56e99b0923a3818680df3b1ffc2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:42.938889Z","signature_b64":"E+rSKDB353pWtKY7UIOIUigD4PLmt0Pu6JEgilK+IKRyxzl+uP/B6vXfqrlQQEbvP/H+kohg7AQ6dyYUmDTrDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72a7a173f26daedca71a5233fbe825881724427f188ec60a4c908a4e0977bb7d","last_reissued_at":"2026-05-18T00:14:42.938111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:42.938111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\varphi(x)=\\varphi_x(x)$. 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