Kashiwara–Vergne and dihedral bigraded Lie algebras in mould theory

Furusho, Hidekazu; Komiyama, Nao

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 32 (2023) no. 4, pp. 655-725

We introduce the Kashiwara–Vergne bigraded Lie algebra associated with a finite abelian group and give its mould theoretic reformulation. By using the mould theory, we show that it includes Goncharov’s dihedral Lie algebra, which generalizes the result of Raphael and Schneps.

Nous introduisons l’algèbre de Lie bi-graduée de Kashiwara–Vergne associée à un groupe fini abélien, et donnons sa reformulation moule-théorique. En utilisant la théorie des moules, nous démontrons que celle-ci inclut l’algèbre de Lie diédrale de Goncharov, généralisant ainsi un résultat de Raphael et Schneps.

Classification : 17B05, 11M32, 16S30, 17B40
Keywords: Kashiwara-Verge Lie algebra, dihedral Lie algebra, mould theory

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