{"paper":{"title":"Simplicity of Lie algebras of Poisson brackets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Adel Alahmadi, Hamed Alsulami","submitted_at":"2019-05-30T10:13:23Z","abstract_excerpt":"Let $A$ be an associative commutative algebra with $1$ over a field of zero characteristic, $\\{,\\} : A \\times A \\to A$ is a Poisson bracket, $Z = \\{ a \\in A \\mid \\{a, A\\} = (0) \\}.$ We prove that if $A$ is simple as a Poisson algebra then the Lie algebra $\\frac{\\{A,A\\}}{\\{A,A\\}\\cap Z}$ is simple."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.13571","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"}