On some algebras related to simple Lie triple systems

The set Hom(DerT)(T x(F) T, T) is determined for any simple finite dimensio nal 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 simp le Jordan algebra. In particular this provides a new proof of the determina tion by Laquer of the invariant affine connections in the simply connected compact irreducible Riemannian symmetric spaces. (C) 1999 Academic Press.