Double derivations of $n-$Hom-Lie color algebras

Abstract

We study the double derivation algebra D(L) of n−Hom Lie color algebra L and describe the relation between D(L) and the usual derivation Hom-Lie color algebra Der(L). We prove that the inner derivation algebra Inn(L) is an ideal of the double derivation algebra D(L). We also show that if L is a perfect n−Hom Lie color algebra with certain constraints on the base field, then the centralizer of Inn(L) in D(L) is trivial. In addition, we obtain that for every centerless perfect n−Hom Lie color algebra L, the triple derivations of the derivation algebra Der(L) are exactly the derivations of Der(L).