NON-DEGENERATE INVARIANT BILINEAR FORMS ON NONASSOCIATIVE TRIPLE SYSTEMS

A bilinear form f on a nonassociative triple system is said to be invariant if and only if f( ,d)=f(a, )=f(c, ) for all . is called a pseudo-metric triple system if f is non-degenerate and invariant. A decomposition theory for triple systems and pseudo-metric triple systems is established. Moreover, the finite-dimensional metric Lie triple systems are characterized in terms of the structure of the non-degenerate, invariant and symmetric bilinear forms on them.