  We give an overview of what is known on Lie groups admitting a left-invariant
metric of negative Ricci curvature, including many natural questions and
conjectures in the solvable case. We also introduce an open and convex cone
C(n) of derivations attached to each nilpotent Lie algebra n, which is defined
as the image of certain moment map and parametrizes a set of solvable Lie
algebras with nilradical n admitting Ricci negative metrics.
