  In this paper, we study admissible $\omega$-left-symmetric algebraic
structures on $\omega$-Lie algebras over the complex numbers field $\mathbb C$.
Based on the classification of $\omega$-Lie algebras, we prove that any perfect
$\omega$-Lie algebra can't be the $\omega$-Lie algebra defined by the
commutator of an $\omega$-left-symmetric algebra.
