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arXiv · 1708.05059

The ascending central series of nilpotent Lie algebras with complex structure

A. Latorre·L. Ugarte·R. Villacampa
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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 $(\mathfrak g, J)$.

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A. Latorre, L. Ugarte, R. Villacampa. 2017-08-16. The ascending central series of nilpotent Lie algebras with complex structure. https://arxiv.org/abs/1708.05059

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