{"paper":{"title":"Braided Weyl algebras and differential calculus on U(u(2))","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"D. Gurevich, P.Pyatov, P.Saponov","submitted_at":"2011-12-29T09:44:32Z","abstract_excerpt":"On any Reflection Equation algebra corresponding to a skew-invertible Hecke symmetry (i.e. a special type solution of the Quantum Yang-Baxter Equation) we define analogs of the partial derivatives. Together with elements of the initial Reflection Equation algebra they generate a \"braided analog\" of the Weyl algebra. When $q\\to 1$, the braided Weyl algebra corresponding to the Quantum Group $U_q(sl(2))$ goes to the Weyl algebra defined on the algebra $\\Sym((u(2))$ or that $U(u(2))$ depending on the way of passing to the limit. Thus, we define partial derivatives on the algebra $U(u(2))$, find t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6258","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"}