On linearised and elliptic versions of the Kashiwara-Vergne Lie algebra
Résumé
The goal of this article is to define a linearized or depth-graded version lkv, and a closely related elliptic version krv ell , of the Kashiwara-Vergne Lie algebra krv originally constructed by Alekseev and Torossian as the space of solutions to the linearized Kashiwara-Vergne problem. We show how the elliptic Lie algebra krv ell is related to earlier constructions of elliptic versions grt ell and ds ell of the Grothendieck-Teichmüller Lie algebra grt and the double shuffle Lie algebra ds. In particular we show that there is an injective Lie morphism ds ell → krv ell , and an injective Lie algebra morphism krv → krv ell extending the known morphisms grt → grt ell (Enriquez section) and ds → ds ell (Écalle map).
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)
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