{"paper":{"title":"Nichols algebras over classical Weyl groups, Fomin-Kirillov algebras and Lyndon basis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Shouchuan Zhang, Weicai Wu, Yao-Zhong Zhang, Zhengtang Tan","submitted_at":"2013-07-31T05:45:07Z","abstract_excerpt":"We show that except in several cases conjugacy classes of classical Weyl groups $W(B_n)$ and $W(D_n)$ are of type {\\rm D}. We prove that except in three cases Nichols algebras of irreducible Yetter-Drinfeld ({\\rm YD} in short )modules over the classical Weyl groups are infinite dimensional. We establish the relationship between Fomin-Kirillov algebra $\\mathcal E_n$ and Nichols algebra $\\mathfrak{B} ({\\mathcal O}_{{(1, 2)}} , \\epsilon \\otimes {\\rm sgn})$ of transposition over symmetry group by means of quiver Hopf algebras. We generalize {\\rm FK } algebra. The characteristic of finiteness of Ni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8227","kind":"arxiv","version":5},"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"}