{"paper":{"title":"Representations of the q-deformed algebra U'_q(so_4)","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"A. U. Klimyk, M. Havlicek, S. Posta","submitted_at":"2001-02-05T09:08:25Z","abstract_excerpt":"We study the nonstandard $q$-deformation $U'_q({\\rm so}_4)$ of the universal enveloping algebra $U({\\rm so}_4)$ obtained by deforming the defining relations for skew-symmetric generators of $U({\\rm so}_4)$. This algebra is used in quantum gravity and algebraic topology. We construct a homomorphism $\\phi$ of $U'_q({\\rm so}_4)$ to the certain nontrivial extension of the Drinfeld--Jimbo quantum algebra $U_q({\\rm sl}_2)^{\\otimes 2}$ and show that this homomorphism is an isomorphism. By using this homomorphism we construct irreducible finite dimensional representations of the classical type and of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0102036","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"}