论文标题
分层谎言代数上的复杂结构
Complex structures on stratified Lie algebras
论文作者
论文摘要
本文研究了代数的复杂结构的一些特性。特别是，我们专注于$ \ textit {nilpotent} $ \ textit {复杂结构} $，其特征在于合适的$ j $ invariant上升或下降中央系列$ \ mathfrak {d}^j $和$ \ m m mathfrak {d} _j _j $。在本文中，我们介绍了一个新的下降系列$ \ mathfrak {p} _j $，并用它来证明nilpotent复杂结构的新表征。我们还检查了分层谎言代数上的nilpotent复合结构是否保留地层。我们发现，存在一个$ j $ invariant的分层，步骤$ 2 $ nilpotent lie代数具有复杂的结构。
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.
