  In this paper, we first study derivations in non nilpotent Lie triple
algebras. We determine the structure of derivation algebra according to whether
the algebra admits an idempotent or a pseudo-idempotent. We study the
multiplicative structure of non nilpotent dimensionally nilpotent Lie triple
algebras. We show that when $n=2p+1$ the adapted basis coincides with the
canonical basis of the gametic algebra $G(2p+2,2)$ or this one obviously
associated to a pseudo-idempotent and if $n=2p$ then the algebra is either one
of the precedent case or a conservative Bernstein algebra.
