On Ricci negative Lie groups

JORGE LAURET; CYNTHIA WILL

Congreso; THE ABEL SYMPOSIUM 2019; 2019

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 con-jectures in the solvable case. We also introduce an open and convex cone C(n) of deriva-tions attached to each nilpotent Lie algebra n, which is dened as the image of a momentmap and parametrizes a set of solvable Lie algebras with nilradical n admitting Ricci neg-ative metrics.