{"paper":{"title":"The universal enveloping algebra of $\\mathfrak{sl}_2$ and the Racah algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Hau-wen Huang, Sarah Bockting-Conrad","submitted_at":"2019-07-03T21:12:48Z","abstract_excerpt":"Let $\\mathbb{F}$ denote a field with ${\\rm char\\,}\\mathbb{F}\\not=2$. The Racah algebra $\\Re$ is the unital associative $\\mathbb{F}$-algebra defined by generators and relations in the following way. The generators are $A$, $B$, $C$, $D$. The relations assert that \\begin{equation*} [A,B]=[B,C]=[C,A]=2D \\end{equation*} and each of the elements \\begin{gather*} \\alpha=[A,D]+AC-BA, \\qquad \\beta=[B,D]+BA-CB, \\qquad \\gamma=[C,D]+CB-AC \\end{gather*} is central in $\\Re$. Additionally the element $\\delta=A+B+C$ is central in $\\Re$.\n  In this paper we explore the relationship between the Racah algebra $\\R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02135","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"}