{"paper":{"title":"On derivations of parabolic Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Daniel Brice","submitted_at":"2015-04-30T16:00:37Z","abstract_excerpt":"Let $\\mathfrak{g}$ be a reductive Lie algebra over an algebraically closed, characteristic zero field or over $\\mathbb{R}$. Let $\\mathfrak{q}$ be a parabolic subalgebra of $\\mathfrak{g}$. We characterize the derivations of $\\mathfrak{q}$ by decomposing the derivation algebra as the direct sum of two ideals: one of which being the image of the adjoint representation and the other consisting of all linear transformations on $\\mathfrak{q}$ that map into the center of $\\mathfrak{q}$ and map the derived algebra of $\\mathfrak{q}$ to $0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08286","kind":"arxiv","version":3},"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"}