We introduce elementary and Ф-free Lie triple systems and study the properties of these systems. In particular, structures of subsystems of an elementary Lie triple system and a class of Ф-free Lie triple systems are investigated.
In this paper, the authors define the center of a Symplectic ternary algebra, and investigate the relationship between the center of a Symplectic ternary algebra and that of the Lie triple system associated with it. As an application of the relationship, the unique decomposition theorem for Symplectic ternary algebras with trivial center is obtained.
