  The present paper is devoted to provide conditions for the Levi--Malcev
theorem to hold or not to hold (i.e. for two Levi subalgebras to be or not
conjugate by an inner automorphism) in the context of finite-dimensional
Leibniz algebras over a field of characteristic zero. Particularly, in the case
of the field $\mathbb{C}$ of complex numbers, we consider all possible cases in
which Levi subalgebras are conjugate and not conjugate.

Representation Theory;Rings and Algebras