Generalized derivations of Hom–Poisson color algebras

In this paper we study some basic properties of the generalized derivation algebra of a multiplicative Hom–Poisson color algebra. Furthermore, we give the definitions of the generalized derivations, quasiderivations, center derivations, centroid and quasicentroid derivations of the multiplicative Hom–Poisson color algebra P.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {P}}.$$\end{document} In particular, we give some useful properties and connections between these derivations. We also prove that QDer(P)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$QDer({\mathcal {P}})$$\end{document} can be embedded as derivations in a larger multiplicative color Hom–Poisson algebra. Finally, we conclude that the derivation of the larger multiplicative color Hom–Poisson algebra has a direct sum decomposition when P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {P}}$$\end{document} is centerless.