{"paper":{"title":"A $\\mathbb{Z}_4^3$-grading on a 56-dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type E","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alberto Elduque, Diego Aranda, Mikhail Kochetov","submitted_at":"2013-12-04T09:04:53Z","abstract_excerpt":"We describe two constructions of a certain $\\mathbb{Z}_4^3$-grading on the so-called Brown algebra (a simple structurable algebra of dimension 56 and skew-dimension 1) over an algebraically closed field of characteristic different from 2 and 3. We also show how this grading gives rise to several interesting fine gradings on exceptional simple Lie algebras of types E6, E7 and E8."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1067","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"}