Double shuffle and Kashiwara–Vergne Lie algebras

We prove that the double shuffle Lie algebra ds, dual to the space of new formal multiple zeta values, injects into the Kashiwara–Vergne Lie algebra krv2 defined and studied by Alekseev and Torossian. The proof is based on a reformulation of the definition of krv2, and uses a theorem of Ecalle on a property of elements of ds. In the final section, we lift this result to an injection DS↪KRV2 of the corresponding pro-unipotent groups.