Naturally reductive pseudo-riemannian 2-step nilpotent lie groups

Abstract

This paper deals with naturally reductive pseudo-Riemannian 2- step nilpotent Lie groups for which the metric is invariant under a left action. The case of nondegenerate center is characterized as follows. The simply connected Lie group can be constructed starting from a real representation of a certain Lie algebra which carries an ad-invariant metric. Also a naturally reductive homogeneous structure is given and applications are shown.