{"paper":{"title":"The double shuffle Lie algebra injects into the Kashiwara-Vergne Lie algebra","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Leila Schneps","submitted_at":"2025-04-19T13:39:05Z","abstract_excerpt":"In this article we prove that there exists an injective Lie morphism from the double shuffle Lie algebra ${\\frak{ds}}$ into the Kashiwara-Vergne Lie algebra ${\\frak{krv}}$, forming a commutative triangle with the known Lie injections of the Grothendieck-Teichm\\\"uller Lie algebra ${\\frak{grt}}\\rightarrow {\\frak{ds}}$ and ${\\frak{grt}}\\rightarrow{\\frak{krv}}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.14293","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/2504.14293/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"}