A complete classification of four-dimensional paraKähler Lie algebras

Abstract

We consider paraKähler Lie algebras, that is, even-dimensional Lie algebras g equipped with a pair (J, g), where J is a paracomplex structure and g a pseudo-Riemannian metric, such that the fundamental 2-form Ω(X, Y) = g(X, JY) is symplectic. A complete classification is obtained in dimension four.

Keywords

• Lie algebras
• paraKähler structures
• pseudo-Riemannian homogeneous spaces