No abstract

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=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.

No abstract

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.

We pointed out the class of Leibniz algebras such that the Killing form is non degenerate implies algebras are semisimple.