{"paper":{"title":"Lie-orthogonal operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Dmytro R. Popovych","submitted_at":"2011-09-07T19:47:24Z","abstract_excerpt":"Basic properties of Lie-orthogonal operators on a finite-dimensional Lie algebra are studied. In particular, the center, the radical and the components of the ascending central series prove to be invariant with respect to any Lie-orthogonal operator. Over an algebraically closed field of characteristic 0, only solvable Lie algebras with solvability degree not greater than two admit Lie-orthogonal operators whose all eigenvalues differ from 1 and -1. The main result of the paper is that Lie-orthogonal operators on a simple Lie algebra are exhausted by the trivial ones. This allows us to give th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1548","kind":"arxiv","version":2},"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"}