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.
Complex symplectic structures on Lie algebras
Bazzoni G;
2021-01-01
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.
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