Symplectic Lie Groups I-III

2013/07/05 by Oliver Baues, Vicente Cortés, Baues, Oliver +1
Mathematics · #(22E25 #53C30 #53D05 #53D20) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1307.1629

openalex publication_date 2013/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop the structure theory of symplectic Lie groups based on the study of their isotropic normal subgroups. The article consists of three main parts. In the first part we show that every symplectic Lie group admits a sequence of subsequent symplectic reductions to a unique irreducible symplectic Lie group. The second part concerns the symplectic geometry of cotangent symplectic Lie groups and the theory of Lagrangian extensions of flat Lie groups. In the third part of the article we analyze the existence problem for Lagrangian normal subgroups in nilpotent symplectic Lie groups.

Citations

• Complex structures on nilpotent Lie algebras
• Symplectic manifolds and their lagrangian submanifolds

Related

• Eight-Dimensional Symplectic Nilpotent Lie Groups with Lagrangian Normal Subgroups: A Complete Classification
• Structure of Symplectic Lie groups and momentum map
• Symplectic or contact structures on Lie Groups
• Flat symplectic Lie algebras
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