On Some Algebras Related to Simple Lie Triple Systems

The set HomDer T(T FT, T) is determined for any simple finite dimensional Lie triple system T over a field F of characteristic zero. It turns out that it contains nontrivial elements if and only if T is related to a simple Jordan algebra. In particular this provides a new proof of the determination by Laquer of the invariant affine connections in the simply connected compact irreducible Riemannian symmetric spaces