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