{"paper":{"title":"On the classification of rational four-dimensional unital division algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Gustav Hammarhjelm","submitted_at":"2018-02-23T12:53:32Z","abstract_excerpt":"In a paper by E. Dieterich 2017, the category $\\mathscr{C}(k)$ of four-dimensional unital division algebras, whose right nucleus is non-trivial and whose automorphism group contains Klein's four group $V$, is studied over a general ground field $k$ with $\\mathrm{char}\\,k\\neq 2$. In particular, the objects in $\\mathscr{C}(k)$ are exhaustively constructed from parameters in $k^3$ and explicit isomorphism conditions for the constructed objects are found in terms of these parameters.\n  In this paper, we specialize to the case $k=\\mathbb{Q}$ and present results towards a classification of $\\mathscr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08507","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"}