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no. 4
Kashiwara–Vergne and dihedral bigraded Lie algebras in mould theory
Hidekazu Furusho1; Nao Komiyama2
1 Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8602, Japan
2 Department of Mathematics, Graduate School of Science, Osaka University Toyonaka, Osaka 560-0043, Japan
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 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.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1749
Classification: 17B05, 11M32, 16S30, 17B40
Keywords: Kashiwara-Verge Lie algebra, dihedral Lie algebra, mould theory

Hidekazu Furusho 1; Nao Komiyama 2

1 Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8602, Japan
2 Department of Mathematics, Graduate School of Science, Osaka University Toyonaka, Osaka 560-0043, Japan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Hidekazu Furusho; Nao Komiyama. Kashiwara–Vergne and dihedral bigraded Lie algebras in mould theory. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 32 (2023) no. 4, pp. 655-725. doi : 10.5802/afst.1749. https://afst.centre-mersenne.org/articles/10.5802/afst.1749/

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