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}).

کلیدواژه ها:

Derivations ، Double derivations ، Inner derivations ، n-Hom-Lie color algebras