We explain the current situation of the relationship between the Kashiwara-Vergne Lie algebra \(\mathfrak {krv}\) and the double shuffle Lie algebra \(\mathfrak {dmr}\) . We also show the validity of Ecalle’s senary relation for small depths.

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Notes on Kashiwara-Vergne and Double Shuffle Lie Algebras

  • Hidekazu Furusho,
  • Nao Komiyama

摘要

We explain the current situation of the relationship between the Kashiwara-Vergne Lie algebra \(\mathfrak {krv}\) and the double shuffle Lie algebra \(\mathfrak {dmr}\) . We also show the validity of Ecalle’s senary relation for small depths.