  The goal of this article is to define a linearized or depth-graded version
$\mathfrak{lkv}$, and a closely related elliptic version
$\mathfrak{krv}_{ell}$, of the Kashiwara-Vergne Lie algebra $\mathfrak{krv}$
originally constructed by Alekseev and Torossian as the space of solutions to
the linearized Kashiwara-Vergne problem. We show how the elliptic Lie algebra
$\mathfrak{krv}_{ell}$ is related to earlier constructions of elliptic versions
$\mathfrak{grt}_{ell}$ and $\mathfrak{ds}_{ell}$ of the
Grothendieck-Teichm\"uller Lie algebra $\mathfrak{grt}$ and the double shuffle
Lie algebra $\mathfrak{ds}$. In particular we show that there is an injective
Lie morphism $\mathfrak{ds}_{ell}\hookrightarrow \mathfrak{krv}_{ell}$, and an
injective Lie algebra morphism $\mathfrak{krv}\rightarrow \mathfrak{krv}_{ell}$
extending the known morphisms
$\mathfrak{grt}\hookrightarrow\mathfrak{grt}_{ell}$ (Enriquez section) and
$\mathfrak{ds}\rightarrow\mathfrak{ds}_{ell}$ (\'Ecalle map).
