{"paper":{"title":"Non-Semisimple Planar Algebras from the Representation Theory of $\\bar{U}_{q}(\\mathfrak{sl}_{2})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.RT"],"primary_cat":"math.QA","authors_text":"Stephen Moore","submitted_at":"2017-03-01T12:49:31Z","abstract_excerpt":"We describe the generators and prove a number of relations for the construction of a planar algebra from the restricted quantum group $\\bar{U}_{q}(\\mathfrak{sl}_{2})$. This is a diagrammatic description of $End_{\\bar{U}_{q}(\\mathfrak{sl}_{2})}(X^{\\otimes n})$, where $X:=\\mathcal{X}^{+}_{2}$ is a two dimensional $\\bar{U}_{q}(\\mathfrak{sl}_{2})$ module."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00271","kind":"arxiv","version":2},"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"}