Complex structures on nilpotent Lie algebras with one-dimensional center

TL;DR

This paper classifies 8-dimensional nilpotent Lie algebras with minimal center that admit complex structures and describes the space of such structures, providing a comprehensive understanding of their geometric properties.

Contribution

It provides a complete classification of 8-dimensional nilpotent Lie algebras with minimal center admitting complex structures and characterizes their complex structure spaces.

Findings

Classified all 8-dimensional nilpotent Lie algebras with minimal center admitting complex structures.

Described the space of complex structures on these algebras up to isomorphism.

Classified nilpotent Lie algebras with non-trivial abelian J-invariant ideals up to eight dimensions.

Abstract

We classify the nilpotent Lie algebras of real dimension eight and minimal center that admit a complex structure. Furthermore, for every such nilpotent Lie algebra $\mathfrak{g}$, we describe the space of complex structures on $\mathfrak{g}$ up to isomorphism. As an application, the nilpotent Lie algebras having a non-trivial abelian $J$-invariant ideal are classified up to eight dimensions.