{"paper":{"title":"The $q$-Onsager algebra and the positive part of $U_q({\\widehat{\\mathfrak{sl}}}_2)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Paul Terwilliger","submitted_at":"2015-06-29T14:56:26Z","abstract_excerpt":"The positive part $U^+_q$ of $U_q({\\widehat{\\mathfrak{sl}}}_2)$ has a presentation by two generators $X,Y$ that satisfy the $q$-Serre relations. The $q$-Onsager algebra $\\mathcal O_q$ has a presentation by two generators $A,B$ that satisfy the $q$-Dolan/Grady relations. We give two results that describe how $U^+_q$ and $\\mathcal O_q$ are related. First, we consider the filtration of $\\mathcal O_q$ whose $n$th component is spanned by the products of at most $n$ generators. We show that the associated graded algebra is isomorphic to $U^+_q$. Second, we introduce an algebra $\\square_q$ and show h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08666","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"}