{"paper":{"title":"Brunnian braids and the inclusion from double shuffle Lie algebra to Kashiwara-Vergne Lie algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.QA","authors_text":"Muze Ren","submitted_at":"2026-05-20T07:33:35Z","abstract_excerpt":"It is proved by L.~Schneps that the double shuffle Lie algebra $\\mathfrak{dmr}_0$ injects to the Kashiwara-Vergne Lie algebra $\\mathfrak{krv}_2$ in \\cite{Schneps2012,Schneps2025}. We show that $\\mathfrak{dmr}_0$ with the infinitesimal hexagon equation $[x,\\varphi(-x,-y,x)]+[y,\\varphi(-x-y,y)]=0$ injects to the symmetric Kashiwara-Vergne Lie algebra $\\mathfrak{krv}^{\\mathrm{sym}}_2$. The proof is based on the inclusion of brunnian braids group on different genus 0 surfaces which is different from the method of mould calculus in \\cite{Schneps2012,Schneps2025}.\n  We generalize the inclusion in tw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20844","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.20844/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}