{"paper":{"title":"A KLR Grading of the Brauer Algebras","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ge Li","submitted_at":"2014-09-03T18:51:31Z","abstract_excerpt":"We construct a naturally $\\mathbb Z$-graded algebra $\\mathscr G_n(\\delta)$ over $R$ with KLR-like relations and give an explicit isomorphism between $\\mathscr G_n(\\delta)$ and $\\mathscr B_n(\\delta)$, the Brauer algebras over $R$, when $R$ is a field of characteristic 0. This isomorphism allows us to exhibit a non-trivial $\\mathbb Z$-grading on the Brauer algebras over a field of characteristic 0. As a byproduct of the proof, we also construct an explicit homogeneous cellular basis for $\\mathscr G_n(\\delta)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1195","kind":"arxiv","version":2},"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"}