{"paper":{"title":"Yang Baxter maps with first degree polynomial 2 by 2 Lax matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Theodoros E. Kouloukas, Vassilios G. Papageorgiou","submitted_at":"2009-03-10T17:57:44Z","abstract_excerpt":"A family of nonparametric Yang Baxter (YB) maps is constructed by refactorization of the product of two 2 by 2 matrix polynomials of first degree. These maps are Poisson with respect to the Sklyanin bracket. For each Casimir function a parametric Poisson YB map is generated by reduction on the corresponding level set. By considering a complete set of Casimir functions symplectic multiparametric YB maps are derived. These maps are quadrirational with explicit formulae in terms of matrix operations. Their Lax matrices are, by construction, 2 by 2 first degree polynomial in the spectral parameter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.1827","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"}