Eight-Dimensional Symplectic Nilpotent Lie Groups with Lagrangian Normal Subgroups: A Complete Classification

2025/08/23 by Aissa, T. Aït, Mansouri, M. W.
#17B05 #17B30 #22E60 #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2508.16978

Abstract

We investigate symplectic nilpotent Lie groups with Lagrangian normal subgroups. We show that there exists a bijection between the isomorphism classes of nilpotent Lie groups with Lagrangian normal subgroups and the isomorphism classes of geodesically complete, flat, nilpotent Lie groups with Lagrangian extension cohomology class. Finally, we provide a complete classification of eight-dimensional symplectic nilpotent Lie groups with Lagrangian normal subgroups, identifying exactly ninety-five such groups. As a consequence, we obtain a complete classification of eight-dimensional symplectic filiform real Lie groups.

Citations

• A complete classification of symplectic forms on six-dimensional Frobeniusian real Lie algebras
• Eight-dimensional symplectic non-solvable Lie algebras
• Symplectic Lie algebras with degenerate center
• Symplectic or contact structures on Lie Groups

Related

• Symplectic Lie Groups I-III
• Lattices in some Symplectic or Affine Nilpotent Lie groups
• Symplectic or contact structures on Lie Groups
• Structure of Symplectic Lie groups and momentum map
• Geometry of Certain Lie-Frobenius Groups