double derivations of $n$-hom-lie color algebras

This paper aims to study the double derivation algebra ${mathcal d}(mathcal{l})$ of $n$-hom-lie color algebra $mathcal{l}$ and describe the relation between ${mathcal d}(mathcal{l})$ and the usual derivation hom-lie color algebra $der(mathcal{l})$. we prove that the inner derivation algebra $inn(mathcal{l})$ is an ideal of the double derivation algebra ${mathcal d}(mathcal{l})$. we also show that if $mathcal{l}$ is a perfect $n$-hom lie color algebra with certain constraints on the base field, then the centralizer of $inn(mathcal{l})$ in ${mathcal d}(mathcal{l})$ is trivial. in addition, we obtain that for every centerless perfect $n$-hom-lie color algebra $mathcal{l}$, the triple derivations of the derivation algebra $der(mathcal{l})$ are exactly the derivations of $der(mathcal{l})$.