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

Dimensionally nilpotent Lie triple algebra pseudo-idempotent Jordan algebra ascending basis