{"paper":{"title":"Divergence and q-divergence in depth 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Anna Lachowska, Anton Alekseev, Elise Raphael","submitted_at":"2014-12-10T14:45:04Z","abstract_excerpt":"The Kashiwara-Vergne Lie algebra $\\mathfrak{krv}$ encodes symmetries of the Kashiwara-Vergne problem on the properties of the Campbell-Hausdorff series. It is conjectures that $\\mathfrak{krv} \\cong \\mathbb{K}t \\oplus \\mathfrak{grt}_1$, where $t$ is a generator of degree 1 and $\\mathfrak{grt}_1$ is the Grothendieck-Teichm\\\"uller Lie algebra. In the paper, we prove this conjecture in depth 2. The main tools in the proof are the divergence cocycle and the representation theory of the dihedral group $D_{12}$. Our calculation is similar to the calculation by Zagier of the graded dimensions of the d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3323","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"}