On The Structure Of Symplectic Ternary Algebras

In this paper ,we discuss the derivations of the symplectic ternary algebras,the correspondence between the trace form of a Lie triple system and that of a symplectic ternary algebra ,and the wedderburn principal theorem . we make use of the relationships among Lie algebras ,Lie triple systems and syrnplectic ternary algebras to investigate it. The conclusions are every derivation of a semi-simple sympleetic ternary algebra has the form of >3 A(x,y); the trace form of a symplectic ternary algebra and the trace form of Lie triple system (associated with )are non-degenerate at the same time ; unitary symplectic ternary algebras can be decomposed into the direct sum of radical and a sub-algebra.