Complex symplectic structures on Lie algebras

2018/11/14 by Giovanni Bazzoni, Marco Freibert, Bazzoni, Giovanni +5 · 2 citations
Mathematics · #22E25 #53C50 #53C56 #53D05 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.CV #math.DG #math.SG #msc:22E25 #msc:53C50 #msc:53C56 #msc:53D05

paper · pdf · doi:10.48550/arxiv.1811.05969

35 pages; comments are welcome

arxiv created 2018/11/14 · arxiv updated 2018/11/16

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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