Lie algebra extensions related with linear bundles of Lie brackets

We consider some special type extensions of an arbitrary Lie algebra ${\cal G}$,arisinginthetheoryofLie-Poissonstructuresover$({\cal G}^*)^n$, where ${\mathcal{G}}^{\ast }$ is the dual of $\mathcal{G}$. We show that some classes of these extensions can be constructed in a natural way using some linear bundles of Lie algebras.