Doubt about nilpotency of the derived algebra of a Leibniz algebra

Question

I want to proof:

"Let $(L,[\cdot,\cdot])$ be a (right or left) Leibniz algebra. If $[L,L]$ is nilpotent then $L$ is solvable".

I know that a similar result is posted for Lie algebras. But here we get a more general context with the Leibniz algebras.

Thanks in advance!

Answer 1

This is only true for finite-dimensional algebras over a field of characteristic zero. It follows from a weak version of Lie's Theorem for Leibniz algebras, see Corollary $6$ in the paper On some basic properties of Leibniz algebras by V. Gorbatsevich.