{"paper":{"title":"What can we learn from Knizhnik--Zamolodchikov Equations?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Dirk Kreimer","submitted_at":"2014-07-19T06:16:01Z","abstract_excerpt":"We discuss structural similarities between Knizhnik--Zamolodchikov equations (in fact, their simplest version needed to introduce the Drinfeld associator) and Dyson--Schwinger equations. We emphasize that the latter allow for a filtration by co-radical degree using quasi-shuffle products and the lower central series filtration of the Lie algebra of Feynman graphs. This clarifies how they are a generalization of the KZ equations. This is a starting point for a algebraic organization of the next-to...-to leading log expansion which has been worked out in collaboration with Olaf Krueger and which"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5150","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"}