Generalized derivations of multiplicative $n$-ary Hom-$\Omega$ color algebras

TL;DR

This paper extends the theory of generalized derivations to multiplicative $n$-ary Hom-$\

Contribution

It introduces new properties and embedding results for generalized derivations in multiplicative $n$-ary Hom-$\

Findings

Generalized derivations have specific algebraic properties.

Quasiderivations can be embedded into larger derivation algebras.

The work generalizes previous results to a broader class of algebras.

Abstract

We generalize the results of Leger and Luks, Zhang R. and Zhang Y.; Chen, Ma, Ni, Niu, Zhou and Fan; Kaygorodov and Popov about generalized derivations of color $n$-ary algebras to the case of $n$-ary Hom-$\Omega$ color algebras. Particularly, we prove some properties of generalized derivations of multiplicative $n$-ary Hom-$\Omega$ color algebras. Moreover, we prove that the quasiderivation algebra of any multiplicative $n$-ary Hom-$\Omega$ color algebra can be embedded into the derivation algebra of a larger multiplicative n-ary Hom-$\Omega$ color algebra.