The ascending central series of nilpotent Lie algebras with complex structure

Abstract

We obtain several restrictions on the terms of the ascending central series of a nilpotent Lie algebra $\mathfrak{g}$ under the presence of a complex structure $J$. In particular, we find a bound for the dimension of the center of $\mathfrak{g}$ 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 $\mathfrak{g}$ admitting this particular type of complex structures $J$. Since our method is constructive, it allows us to describe the complex structure equations that parametrize all such pairs $(\mathfrak{g},J)$.

28 pages, 1 figure. To appear in Trans. Amer. Math. Soc

References in corpus (1)

• 6-dimensional product Lie algebras admitting integrable complex structures