CONICET | Buscador de Institutos y Recursos Humanos

Until a couple of years ago, the only known examples of Lie groups admittingleft-invariant metrics with negative Ricci curvature were either solvable or semisimple. Weuse a general construction from a previous article of the second named author to produce alarge amount of examples with compact Levi factor. Given a compact semisimple real Liealgebra u and a real representation π satisfying some technical properties, the constructionreturns a metric Lie algebra l(u, π) with negative Ricci operator. In this paper, whenu is assumed to be simple, we prove that l(u, π) admits a metric having negative Riccicurvature for all but finitely many finite-dimensional irreducible representations of u⊗RC,regarded as a real representation of u. We also prove in the last section a more generalresult where the nilradical is not abelian, as it is in every l(u, π).