ABSTRACT
We first show that an invariant symmetric bilinear form on a Lie triple system can be uniquely extended to its standard imbedding Lie algebra, and then prove that any Lie triple system over a field of characteristic zero admitting a unique up to a scalar multiple, nondegenerate invariant symmetric bilinear form is necessarily simple. If the field
is algebraically closed, that condition is also sufficent.
ACKNOWLEDGMENT
This work is supported by Natural Science Foundation of Hebei Province (199100).