{"paper":{"title":"Combinatorial aspects of the quantized universal enveloping algebra of $\\mathfrak{sl}_{n+1}(\\mathbb{C})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CO","authors_text":"David M. Jackson, Geoffrey Stanley, Raymond Cheng","submitted_at":"2016-01-07T02:42:19Z","abstract_excerpt":"Quasi-triangular Hopf algebras were introduced by Drinfel'd in his construction of solutions to the Yang--Baxter Equation. This algebra is built upon $\\mathcal{U}_h(\\mathfrak{sl}_2)$, the quantized universal enveloping algebra of the Lie algebra $\\mathfrak{sl}_2$. In this paper, combinatorial structure in $\\mathcal{U}_h(\\mathfrak{sl}_2)$ is elicited, and used to assist in highly intricate calculations in this algebra. To this end, a combinatorial methodology is formulated for straightening algebraic expressions to a canonical form in the case $n=1$. We apply this formalism to the quasi-triangu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01377","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"}