Complex symplectic structures on Lie algebras

2018/11/14 by Bazzoni, Giovanni, Freibert, Marco, Latorre, Adela +1 · 2 citations
#22E25 #53C50 #53C56 #53D05 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1811.05969

Abstract

We investigate Lie algebras endowed with a complex symplectic structure and develop a method, called complex symplectic oxidation, to construct certain complex symplectic Lie algebras of dimension 4n+4 from those of dimension 4n. We specialize this construction to the nilpotent case and apply complex symplectic oxidation to classify eight-dimensional nilpotent complex symplectic Lie algebras.

Cited by

• 8-dimensional 2-step nilpotent Lie algebras over algebraically closed fields of char ≠ 2, 3
• Complex symplectic structures: deformations and cohomology

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