  Based on the relation between the notions of Lie triple systems and Jordan
algebras, we introduce the $n$-ary Jordan algebras,an $n$-ary generalization of
Jordan algebras obtained via the generalization of the following property
$\left[ R_{x},R_{y}\right] \in Der\left( \mathcal{A}\right)$, where
$\mathcal{A}$ is an $n$-ary algebra. Next, we study a ternary example of these
algebras. Finally, based on the construction of a family of ternary algebras
defined by means of the Cayley-Dickson algebras, we present an example of a
ternary $D_{x,y}$-derivation algebra ($n$-ary $D_{x,y}$-derivation algebras are
the non-commutative version of $n$-ary Jordan algebras).
