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Kashiwara–Vergne solutions degree by degree
[Solutions de Kashiwara–Vergne degré par degré]
Comptes Rendus. Mathématique, Volume 363 (2025), pp. 777-789.

We show that solutions to the Kashiwara–Vergne problem can be extended degree by degree. This can be used to simplify the computation of a class of Drinfel’d associators, which under the Alekseev–Torossian conjecture, may comprise all associators. We also give a proof that the associated graded Lie algebra of the Kashiwara–Vergne group is isomorphic to the graded Kashiwara–Vergne Lie algebra.

Nous montrons que les solutions au problème de Kashiwara–Vergne peuvent être étendues degré par degré. Ce résultat peut être utilisé pour simplifier le calcul d’une classe d’associateurs de Drinfel’d, qui d’après une conjecture d’Alekseev–Torossian pourrait comprendre tous les associateurs. Nous montrons également que l’algèbre de Lie graduée associée au groupe de Kashiwara–Vergne est isomorphe à l’algèbre de Lie du groupe de Kashiwara–Vergne gradué.

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DOI : 10.5802/crmath.750
Classification : 17B01, 17B45, 57K12

Zsuzsanna Dancso 1 ; Iva Halacheva 2 ; Guillaume Laplante-Anfossi 3 ; Marcy Robertson 3

1 School of Mathematics and Statistics, The University of Sydney, Sydney, New South Wales, Australia
2 Department of Mathematics, Northeastern University, Boston, Massachusetts, USA
3 School of Mathematics and Statistics, The University of Melbourne, Melbourne, Victoria, Australia
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Kashiwara{\textendash}Vergne solutions degree by degree},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {777--789},
     publisher = {Acad\'emie des sciences, Paris},
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     year = {2025},
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Zsuzsanna Dancso; Iva Halacheva; Guillaume Laplante-Anfossi; Marcy Robertson. Kashiwara–Vergne solutions degree by degree. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 777-789. doi : 10.5802/crmath.750. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.750/

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