Complex structures on nilpotent Lie algebras with one-dimensional center

We classify the nilpotent Lie algebras of real dimension eight and minimal center that admit a complex structure. Further-more, for every such nilpotent Lie algebra g, we describe the space of complex structures on g up to isomorphism. As an application, the nilpotent Lie algebras having a non-trivial abelian J-invariant ideal are classified up to eight dimensions. (C) 2022 Elsevier Inc. All rights reserved.

Automated summary

This article investigates nilpotent Lie algebras of real dimension eight and minimal center that admit a complex structure. Furthermore, for each such nilpotent Lie algebra g, the space of complex structures on g is described up to isomorphism. As an application, the classification of nilpotent Lie algebras with non-trivial abelian J-invariant ideals is provided up to eight dimensions.