Classification of Orbit Closures in the Variety of 4-Dimensional Symplectic Lie Algebras

Abstract

The aim of this paper is to study the natural action of the real symplectic group, Sp (4 , R) , on the algebraic set of 4-dimensional Lie algebras admitting symplectic structures and to give a complete classification of orbit closures. We present some applications of such classification to the study of the Ricci curvature of left-invariant almost Kähler structures on four dimensional Lie groups.