A classification of left-invariant symplectic structures on some Lie groups

2020/12/03 by Moscoso, Luis Pedro Castellanos, Tamaru, Hiroshi · 3 citations
#22E25(Secondary) #53C30(Primary) #53D05(Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2012.01710

Abstract

We are interested in the classification of left-invariant symplectic structures on Lie groups. Some classifications are known, especially in low dimensions. In this paper we establish a new approach to classify (up to automorphism and scale) left-invariant symplectic structures on Lie groups. The procedure is based on the moduli space of left-invariant nondegenerate 2-forms. Then we apply our procedure for two particular Lie groups of dimension 2n and give classifications of left-invariant symplectic structures on them.

Cited by

• The moduli spaces of presymplectic forms on almost abelian Lie algebras
• Infinitely many left-symmetric structures on nilpotent Lie algebras
• The moduli spaces of left-invariant statistical structures on Lie groups

Related

• Symplectic or contact structures on Lie Groups
• Structure of Symplectic Lie groups and momentum map
• Classification of complete left-invariant affine structures on the Oscillator group
• Classification of almost abelian Lie groups admitting left-invariant complex or symplectic structures
• Symplectic structures on 2-step nilpotent Lie algebras