Complex structures on stratified Lie algebras

Junze Zhang

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arXiv · 2202.02111

Complex structures on stratified Lie algebras

Junze Zhang

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Abstract

This paper investigates some properties of complex structures on Lie algebras. In particular, we focus on $\textit{nilpotent}$ $\textit{complex structures}$ that are characterized by a suitable $J$-invariant ascending or descending central series $\mathfrak{d}^j$ and $\mathfrak{d}_j$ respectively. In this article, we introduce a new descending series $\mathfrak{p}_j$ and use it to give proof of a new characterization of nilpotent complex structures. We examine also whether nilpotent complex structures on stratified Lie algebras preserve the strata. We find that there exists a $J$-invariant stratification on a step $2$ nilpotent Lie algebra with a complex structure.

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Junze Zhang. 2022-02-04. Complex structures on stratified Lie algebras. https://arxiv.org/abs/2202.02111

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