On the elliptic Kashiwara-Vergne Lie algebra (Q2658273)

The present paper is concerned with a comparison of two definitions of an elliptic Kashiwara-Vergne Lie algebra. Recall that the original Kashiwara-Vergne Lie algebra was introduced by Alekseev-Torossian in the context of the Kashiwara-Vergne conjecture [\textit{M. Kashiwara} and \textit{M. Vergne}, Invent. Math. 47, 249--272 (1978; Zbl 0404.22012)]. Subsequently, two different constructions in genus one were given by \textit{A. Alekseev} et al. [C. R., Math., Acad. Sci. Paris 355, No. 2, 123--127 (2017; Zbl 1420.57052)] and by \textit{E. Raphael} ans \textit{L. Schneps} [``On linearised and elliptic versions of the Kashiwara-Vergne Lie algebra'', Preprint, \url{arXiv:1706.08299}]. In this paper, the authors prove that the two Lie algebras thus obtained are canonically isomorphic to one another. For the entire collection see [Zbl 1459.11005].