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We introduce the Kashiwara-Vergne bigraded Lie algebra associated with afinite abelian group and give its mould theoretic reformulation. By using themould theory, we show that it includes Goncharov's dihedral Lie algebra, whichgeneralizes the result of Raphael and Schneps.

Kashiwara-Vergne and dihedral bigraded Lie algebras in mould theory