{"paper":{"title":"On the definition of quasi-Jordan algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.RA","authors_text":"Murray R. Bremner","submitted_at":"2010-08-11T21:00:13Z","abstract_excerpt":"Velasquez and Felipe recently introduced quasi-Jordan algebras based on the product $a \\triangleleft b = \\tfrac12 ( a \\dashv b + b \\vdash a )$ in an associative dialgebra with operations $\\dashv$ and $\\vdash$. We determine the polynomial identities of degree $\\le 4$ satisfied by this product. In addition to right commutativity and the right quasi-Jordan identity, we obtain a new associator-derivation identity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2009","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"}