{"paper":{"title":"The $q$-Onsager algebra and its alternating central extension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.QA","authors_text":"Paul Terwilliger","submitted_at":"2021-06-26T15:06:08Z","abstract_excerpt":"The $q$-Onsager algebra $O_q$ has a presentation involving two generators $W_0$, $W_1$ and two relations, called the $q$-Dolan/Grady relations. The alternating central extension $\\mathcal O_q$ has a presentation involving the alternating generators $\\lbrace \\mathcal W_{-k}\\rbrace_{k=0}^\\infty$, $\\lbrace \\mathcal W_{k+1}\\rbrace_{k=0}^\\infty$, $ \\lbrace \\mathcal G_{k+1}\\rbrace_{k=0}^\\infty$, $\\lbrace \\mathcal {\\tilde G}_{k+1}\\rbrace_{k=0}^\\infty$ and a large number of relations. Let $\\langle \\mathcal W_0, \\mathcal W_1 \\rangle$ denote the subalgebra of $\\mathcal O_q$ generated by $\\mathcal W_0$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.14041","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.14041/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}