{"paper":{"title":"An action of the free product $\\mathbb Z_2 \\star \\mathbb Z_2 \\star \\mathbb Z_2$ on the $q$-Onsager algebra and its current algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Paul Terwilliger","submitted_at":"2018-08-29T16:06:04Z","abstract_excerpt":"Recently Pascal Baseilhac and Stefan Kolb introduced some automorphisms $T_0$, $T_1$ of the $q$-Onsager algebra $\\mathcal O_q$, that are roughly analogous to the Lusztig automorphisms of $U_q(\\widehat{\\mathfrak{sl}}_2)$. We use $T_0, T_1$ and a certain antiautomorphism of $\\mathcal O_q$ to obtain an action of the free product $\\mathbb Z_2 \\star \\mathbb Z_2 \\star \\mathbb Z_2$ on $\\mathcal O_q$ as a group of (auto/antiauto)-morphisms. The action forms a pattern much more symmetric than expected. We show that a similar phenomenon occurs for the associated current algebra $\\mathcal A_q$. We give s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09901","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"}