  Until a couple of years ago, the only known examples of Lie groups admitting
left-invariant metrics with negative Ricci curvature were either solvable or
semisimple. We use a general construction from a previous article of the second
named author to produce a great amount of examples with compact Levy factor.
Given a compact semisimple real Lie algebra $\mathfrak u$ and a real
representation $\pi$ satisfying some technical properties, the construction
returns a metric Lie algebra $\mathfrak l(\mathfrak u,\pi)$ with negative Ricci
operator. In this paper, when $\mathfrak u$ is assumed to be simple, we prove
that $\mathfrak l(\mathfrak u,\pi)$ admits a metric having negative Ricci
curvature for all but finitely many finite-dimensional irreducible
representations of $\mathfrak u\otimes_{\mathbb R} \mathbb C$, regarded as a
real representation of $\mathfrak u$. We also prove in the last section a more
general result where the nilradical is not abelian, as it is in every
$\mathfrak l(\mathfrak u,\pi)$.
