{"paper":{"title":"The Universal Askey-Wilson Algebra and the Equitable Presentation of $U_q(\\mathfrak{sl}_2)$","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Paul Terwilliger","submitted_at":"2011-07-18T19:51:03Z","abstract_excerpt":"Around 1992 A. Zhedanov introduced the Askey-Wilson algebra AW(3). Recently we introduced a central extension $\\Delta$ of AW(3) called the universal Askey-Wilson algebra. In this paper we discuss a connection between $\\Delta$ and the quantum algebra $U_q(\\mathfrak{sl}_2)$. Our main result is an algebra injection from $\\Delta$ into a relative of $U_q(\\mathfrak{sl}_2)$; the relative is obtained from $U_q(\\mathfrak{sl}_2)$ by adjoining three mutually commuting indeterminates. We describe the injection using the equitable presentation of $U_q(\\mathfrak{sl}_2)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3544","kind":"arxiv","version":3},"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"}