Devivation Algebra And Invariant Symmetric Bilinear Forms Of Lie Triple System

In the presen paPer, we have some discussion on Lie triPle system. We get a con-clusion that if a Lie triPle system T 8atisfying Z(T) = 0 can be decOmposed into the dthectstnn of two ideals, T = T $Tz, then the acconiing derivation algebra has a decompositionD(T) = D(T )$D(T2 ). Thus we can easily obtain the decomposition of derivation alge-hra of a semisimPle lie triple system. For a simPle Lie algebra L, if ft and fz are nonde-generate mptric invariant bilinear form on L, then there is a nonzem scalar a such thatf, = afz. HOW hout this for Lie triPle system? Here, we give a postive answr tO theproblem.