{"paper":{"title":"The simple non-Lie Malcev algebra as a Lie-Yamaguti algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Andrew Douglas, Murray R. Bremner","submitted_at":"2011-08-21T19:46:44Z","abstract_excerpt":"The simple 7-dimensional Malcev algebra $M$ is isomorphic to the irreducible $\\mathfrak{sl}(2,\\mathbb{C})$-module V(6) with binary product $[x,y] = \\alpha(x \\wedge y)$ defined by the $\\mathfrak{sl}(2,\\mathbb{C})$-module morphism $\\alpha\\colon \\Lambda^2 V(6) \\to V(6)$. Combining this with the ternary product $(x,y,z) = \\beta(x \\wedge y) \\cdot z$ defined by the $\\mathfrak{sl}(2,\\mathbb{C})$-module morphism $\\beta\\colon \\Lambda^2 V(6) \\to V(2) \\approx \\s$ gives $M$ the structure of a generalized Lie triple system, or Lie-Yamaguti algebra. We use computer algebra to determine the polynomial identi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4202","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"}