{"paper":{"title":"Rational orbits of the space of pairs of exceptional Jordan algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Akihiko Yukie, Ryo Kato","submitted_at":"2016-03-02T15:12:10Z","abstract_excerpt":"Let $k$ be a field of characteristic not equal to $2,3$, $\\mathbb{O}$ an octonion over $k$ and $\\mathcal{J}$ the exceptional Jordan algebra defined by $\\mathbb{O}$. We consider the prehomogeneous vector space $(G,V)$ where $G=GE_6\\times \\mathrm{GL}(2)$ and $V=\\mathcal{J}\\oplus \\mathcal{J}$. We prove that generic rational orbits of this prehomogeneous vector space are in bijective correspondence with $k$-isomorphism classes of pairs $(\\mathcal{M},\\mathfrak{n})$ where $\\mathcal{M}$'s are isotopes of $\\mathcal{J}$ and $\\mathfrak{n}$'s are cubic \\'etale subalgebras of $\\mathcal{M}$. Also we prove "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00739","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"}