Classification of SNC-algebras in dimension five

Abstract

Every homogeneous manifold of negative curvature is known to be isometric to a Lie group with a left invariant metric. We define an SNC-algebra to be a Lie algebra which admits an inner product of strictly negative curvature. In the author's joint paper in 2022, we classified SNC-algebras in dimension four. In this article, we classify SNC-algebras in dimension five, as well as we calculate Ricci curvature of SNC-algebras in dimension four.