[Solutions de Kashiwara–Vergne degré par degré]
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.
Révisé le :
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Zsuzsanna Dancso 1 ; Iva Halacheva 2 ; Guillaume Laplante-Anfossi 3 ; Marcy Robertson 3

@article{CRMATH_2025__363_G8_777_0, author = {Zsuzsanna Dancso and Iva Halacheva and Guillaume Laplante-Anfossi and Marcy Robertson}, title = {Kashiwara{\textendash}Vergne solutions degree by degree}, journal = {Comptes Rendus. Math\'ematique}, pages = {777--789}, publisher = {Acad\'emie des sciences, Paris}, volume = {363}, year = {2025}, doi = {10.5802/crmath.750}, language = {en}, }
TY - JOUR AU - Zsuzsanna Dancso AU - Iva Halacheva AU - Guillaume Laplante-Anfossi AU - Marcy Robertson TI - Kashiwara–Vergne solutions degree by degree JO - Comptes Rendus. Mathématique PY - 2025 SP - 777 EP - 789 VL - 363 PB - Académie des sciences, Paris DO - 10.5802/crmath.750 LA - en ID - CRMATH_2025__363_G8_777_0 ER -
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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