{"paper":{"title":"Partially Alternative Real Division Algebras With A Few Imaginary Units","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Marina Tvalavadze, Tianran Hua","submitted_at":"2025-07-07T12:05:22Z","abstract_excerpt":"In this paper, we extend the investigation of four-dimensional partially alternative algebras $\\mathcal A$ initiated in \\cite{HNT}. The partial alternativity condition, a natural generalization of the alternativity axiom, broadens the class of alternative algebras, enabling the exploration of non-associative structures with weakened algebraic constraints.\n  We focus on four-dimensional partially alternative real division algebras (RDAs) equipped with at least three distinct imaginary units and a reflection. Under these constraints, we achieve a complete classification of the isomorphism classe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04919","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.04919/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}