{"paper":{"title":"On a conjecture by Pierre Cartier about a group of associators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vincel Hoang Ngoc Minh (LIPN)","submitted_at":"2009-10-10T17:20:41Z","abstract_excerpt":"In \\cite{cartier2}, Pierre Cartier conjectured that for any non commutative formal power series $\\Phi$ on $X=\\{x_0,x_1\\}$ with coefficients in a $\\Q$-extension, $A$, subjected to some suitable conditions, there exists an unique algebra homomorphism $\\varphi$ from the $\\Q$-algebra generated by the convergent polyz\\^etas to $A$ such that $\\Phi$ is computed from $\\Phi_{KZ}$ Drinfel'd associator by applying $\\varphi$ to each coefficient. We prove $\\varphi$ exists and it is a free Lie exponential over $X$. Moreover, we give a complete description of the kernel of polyz\\^eta and draw some consequenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1932","kind":"arxiv","version":10},"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"}