{"paper":{"title":"A differential bialgebra associated to a set theoretical solution of the Yang-Baxter equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Juliana Garc\\'ia Galofre, Marco A. Farinati","submitted_at":"2015-08-31T19:34:22Z","abstract_excerpt":"For a set theoretical solution of the Yang-Baxter equation $(X,\\sigma)$, we define a d.g. bialgebra $B=B(X,\\sigma)$, containing the semigroup algebra $A=k\\{X\\}/\\langle xy=zt : \\sigma(x,y)=(z,t)\\rangle$, such that $k\\otimes_A B\\otimes_Ak$ and $\\mathrm{Hom}_{A-A}(B,k)$ are respectively the homology and cohomology complexes computing biquandle homology and cohomology defined in \\cite{CJKS} and other generalizations of cohomology of rack-quanlde case (for example defined in \\cite{CES}). This algebraic structure allow us to show the existence of an associative product in the cohomology of biquandle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07970","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"}