Non-degenerate bilinear forms and left-symmetric structures

Chu proved that a symplectic structure $ω$ on an even-dimensional Lie algebra induces a left-symmetric structure which is defined by $ω(x\scriptstyleΔ_ω y,z)=-ω(y,[x,z])$. El Bourkadi and Mansouri proved that a cosymplectic structure on an odd-dimensional Lie algebra $\mathfrak{g}$ induces the left-