Representation of reductive Lie algebras

Question

Let $\mathfrak{L}$ be a reductive Lie algebra. Suppose that $\mathfrak{L}$ is a direct sum of $\mathfrak{g}$ and $\mathfrak{h}$ as Lie algebras where $\mathfrak{g}$ is a semisimple Lie algebra and $\mathfrak{h}$ is its center. Is every representation of $\mathfrak{L}$ a tensor product of a representation of $\mathfrak{g}$ and a representation of $\mathfrak{h}$?