{"paper":{"title":"On the quadratic dual of the Fomin-Kirillov algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Chelsea Walton, James J. Zhang","submitted_at":"2018-06-25T02:58:53Z","abstract_excerpt":"We study ring-theoretic and homological properties of the quadratic dual (or Koszul dual) $\\mathcal{E}_n^!$ of the Fomin-Kirillov algebras $\\mathcal{E}_n$; these algebras are connected $\\mathbb{N}$-graded and are defined for $n \\geq 2$. We establish that the algebra $\\mathcal{E}_n^!$ is module-finite over its center (so, satisfies a polynomial identity), is Noetherian, and has Gelfand-Kirillov dimension $\\lfloor n/2 \\rfloor$ for each $n \\geq 2$. We also observe that $\\mathcal{E}_n^!$ is not prime for $n \\geq 3$. By a result of Roos, $\\mathcal{E}_n$ is not Koszul for $n \\geq 3$, so neither is $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09263","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"}