{"paper":{"title":"Characterization of Lie Derivations on von Neumann Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jinchuan Hou, Xiaofei Qi","submitted_at":"2012-05-05T03:14:43Z","abstract_excerpt":"Let ${\\mathcal M}$ be a von Neumann algebra without central summands of type $I_1$ and $\\xi\\in{\\mathbb C}$ a scalar. It is shown that an additive map $L$ on $\\mathcal M$ satisfies $L(AB-\\xi BA)=L(A)B-\\xi BL(A)+L(B)A-\\xi AL(B)$ whenever $A,B\\in{\\mathcal M}$ with $AB=0$ if and only if one of the following statements holds: (1) $\\xi=1$, $L=\\varphi+f$, where $\\varphi$ is an additive derivation on $\\mathcal M$ and $f$ is an additive map from $\\mathcal M$ into its center vanishing on $[A,B]$ with $AB=0$; (2)\n  $\\xi=0$, $L(I)\\in{\\mathcal Z}({\\mathcal M})$ and there exists an additive derivation $\\var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1095","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"}