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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1108.4202","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-08-21T19:46:44Z","cross_cats_sorted":[],"title_canon_sha256":"86925a5d5023fb13042090b6d1dff68e95bcf017a0b04b9485f9c9062f25f317","abstract_canon_sha256":"bb82946a9db9e0047cae67a712e00ddffb67c995d0d4b36f7aa93481be2050e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:55.965095Z","signature_b64":"VNWsEvbb/pHNJ6Y/IVVJWtwA+exKaCM1r3DC1on4o7JqTROVMMdo6+uwVOuMC095TeN7w9TISZcJTwMvL8AGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98dc4735c25e7f853d70163f3c68d5e145fbef6c2066a023877c1aacc0851e07","last_reissued_at":"2026-05-18T04:14:55.964382Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:55.964382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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