N. Kato

Non-degenerate bilinear forms and left-symmetric structures

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