{"paper":{"title":"Root space decomposition of $\\mathfrak{g}_2$ from octonions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Tathagata Basak","submitted_at":"2017-08-08T04:33:54Z","abstract_excerpt":"We describe a simple way to write down explicit derivations of octonions that form a Chevalley basis of $\\mathfrak{g}_2$. This uses the description of octonions as a twisted group algebra of the finite field $\\mathbb{F}_8$. Generators of $\\operatorname{Gal}(\\mathbb{F}_8/\\mathbb{F}_2)$ act on the roots as $120$-degree rotations and complex conjugation acts as negation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02367","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"}