The ascending central series of nilpotent Lie algebras with complex structure

We obtain several restrictions on the terms of the ascending central series of a nilpotent Lie algebra g \mathfrak {g} under the presence of a complex structure J J . In particular, we find a bound for the dimension of the center of g \mathfrak {g} when it does not contain any non-trivial J J -invariant ideal. Thanks to these results, we provide a structural theorem describing the ascending central series of 8-dimensional nilpotent Lie algebras g \mathfrak {g} admitting this particular type of complex structure J J . Since our method is constructive, it allows us to describe the complex structure equations that parametrize all such pairs ( g , J ) (\mathfrak {g}, J) .