Kashiwara–Vergne and dihedral bigraded Lie algebras in mould theory

Hidekazu Furusho; Nao Komiyama

doi:10.5802/afst.1749

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

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

Résumé
Abstract

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.

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.

Reçu le : 2020-12-07
Accepté le : 2021-07-20
Publié le : 2023-11-13

DOI : 10.5802/afst.1749

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

Affiliations des auteurs :

Hidekazu Furusho ¹ ; Nao Komiyama ²

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
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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, Série 6, Tome 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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