Complex symplectic structures on Lie algebras (Q1996042)

A complex symplectic manifold is a smooth manifold with a complex structure and a closed, non-degenerate \((2,0)\)-form. There is a corresponding notion of complex symplectic Lie algebras. The authors give some construction (named as complex symplectic oxidation in analogy with known notion of the symplectic oxidation). This construction (rather bulky) gives a method to construct complex symplectic structures on \((4n+4)\)-dimensional Lie algebras from \(4n\)-dimensional complex symplectic Lie algebras. Then this construction is applied to nilpotent Lie algebras and it is shown that every nilpotent complex symplectic Lie algebra of dimension 4 and 8 can be obtained by oxidating of some nilpotent complex symplectic Lie algebras. Also some results about complex symplectic structures on nilmanifolds and solvmanifolds and some examples of oxidation are considered.