{"paper":{"title":"On equivariant maps related to the space of pairs of exceptional Jordan algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Akihiko Yukie, Ryo Kato","submitted_at":"2016-03-02T15:36:33Z","abstract_excerpt":"Let $\\mathcal{J}$ be the exceptional Jordan algebra and $V=\\mathcal{J}\\oplus \\mathcal{J}$. We construct an equivariant map from $V$ to $\\mathrm{Hom}_k(\\mathcal{J}\\otimes \\mathcal{J},\\mathcal{J})$ defined by homogeneous polynomials of degree $8$ such that if $x\\in V$ is a generic point, then the image of $x$ is the structure constant of the isotope of $\\mathcal{J}$ corresponding to $x$. We also give an alternative way to define the isotope corresponding to a generic point of $\\mathcal{J}$ by an equivariant map from $\\mathcal{J}$ to the space of trilinear forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00753","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"}