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Article Dans Une Revue Journal of Lie Theory Année : 2023

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).
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Dates et versions

hal-02994283 , version 1 (07-11-2020)

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Elise Raphael, Leila Schneps. On linearised and elliptic versions of the Kashiwara-Vergne Lie algebra. Journal of Lie Theory, In press. ⟨hal-02994283⟩
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