{"paper":{"title":"Classification of the algebras $\\mathbb{O}_{p,q}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.AC","authors_text":"Marie Kreusch, Sophie Morier-Genoud","submitted_at":"2013-12-13T20:48:34Z","abstract_excerpt":"We study a series of real nonassociative algebras $\\mathbb{O}_{p,q}$ introduced in $[5]$. These algebras have a natural $\\mathbb{Z}_2^n$-grading, where $n=p+q$, and they are characterized by a cubic form over the field $\\mathbb{Z}_2$. We establish all the possible isomorphisms between the algebras $\\mathbb{O}_{p,q}$ preserving the structure of $\\mathbb{Z}_2^n$-graded algebra. The classification table of $\\mathbb{O}_{p,q}$ is quite similar to that of the real Clifford algebras $\\mathrm{Cl}_{p,q}$, the main difference is that the algebras $\\mathbb{O}_{n,0}$ and $\\mathbb{O}_{0,n}$ are exceptional"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3935","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"}