Lie algebras whose Lie groups have negative sectional curvature

Abstract

The aim of this work is to completely describe two families of Lie algebras whose Lie groups have negative sectional curvature. The first family consists of Lie algebras satisfying the following property: given any two vectors in the Lie algebra, the linear subspace spanned by them is a Lie subalgebra. On the other hand, the second family consists of reduced Lie algebras of Iwasawa type.