Classification of orbit closures in the variety of 4-dimensional symplectic Lie algebras

2023/03/22 by Edison Alberto Fernández-Culma, Fernández-Culma, Edison Alberto, Nadina Rojas +1
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2303.12508

openalex publication_date 2023/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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.

Related

• Hypersymplectic four-dimensional Lie algebras
• On the classification of left-invariant para-Kähler structures on four-dimensional Lie groups
• The classification of left-invariant para-Kähler structures on simply connected four-dimensional Lie groups
• Almost Kähler 4-dimensional Lie groups with J-invariant Ricci tensor
• Symplectic or contact structures on Lie Groups