{"paper":{"title":"Enveloping algebras of the nilpotent Malcev algebra of dimension five","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.RA","authors_text":"Hamid Usefi, Murray R. Bremner","submitted_at":"2010-08-16T18:09:56Z","abstract_excerpt":"Perez-Izquierdo and Shestakov recently extended the PBW theorem to Malcev algebras. It follows from their construction that for any Malcev algebra $M$ over a field of characteristic $\\ne 2, 3$ there is a representation of the universal nonassociative enveloping algebra $U(M)$ by linear operators on the polynomial algebra $P(M)$. For the nilpotent non-Lie Malcev algebra $\\mathbb{M}$ of dimension 5, we use this representation to determine explicit structure constants for $U(\\mathbb{M})$; from this it follows that $U(\\mathbb{M})$ is not power-associative. We obtain a finite set of generators for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2728","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"}