{"paper":{"title":"3D compatible ternary systems and Yang-Baxter maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.QA","nlin.SI"],"primary_cat":"math-ph","authors_text":"Theodoros E. Kouloukas, Vassilios G. Papageorgiou","submitted_at":"2012-03-09T10:56:39Z","abstract_excerpt":"According to Shibukawa, ternary systems defined on quasigroups and satisfying certain conditions provide a way of constructing dynamical Yang-Baxter maps. After noticing that these conditions can be interpreted as 3-dimensional compatibility of equations on quad-graphs, we investigate when the associated dynamical Yang-Baxter maps are in fact parametric Yang-Baxter maps. In some cases these maps can be obtained as reductions of higher dimensional maps through compatible constraints. Conversely, parametric YB maps on quasigroups with an invariance condition give rise to 3-dimensional compatible"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2037","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"}