{"paper":{"title":"Indecomposable decomposition of tensor products of modules over the restricted quantum universal enveloping algebra associated to $\\boldsymbol{\\mathfrak{sl}_2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Hiroki Kondo, Yoshihisa Saito","submitted_at":"2009-01-27T11:13:53Z","abstract_excerpt":"In this paper we study the tensor category structure of the module category of the restricted quantum enveloping algebra associated to $\\mathfrak{sl}_2$. Indecomposable decomposition of all tensor products of modules over this algebra is completely determined in explicit formulas. As a by-product, we show that the module category of the restricted quantum enveloping algebra associated to $\\mathfrak{sl}_2$ is not a braided tensor category."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4221","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"}