论文标题
最大的尼罗氏络合物结构
Maximal nilpotent complex structures
论文作者
论文摘要
让$（\ mathfrak {g}，j）$为nilpotent Lie代数$ \ mathfrak {g} $（简称NLA），并带有Nilpotent复杂结构$ J $。在本文中，是由Cordero，Fernández，Gray和Ugarte的一个问题的动机，我们证明$ 2 \leqν（J）\ leq 3 $ for $（\ Mathfrak {G}，J），J）$ n $ n时，$ν（\ Mathfrak {G} $ \ mathfrak {g} $和$ν（j）$是唯一的最小整数，因此$ \ mathfrak {a}（j）_ {ν（J）} = \ Mathfrak {g} $如Corder，Fernández，Gray，Gray，Gray和Ugarte的定义1和8所示。当$ν（\ Mathfrak {g}）= 3 $，对于任意$ n \ geq 3 $，存在一对$（\ Mathfrak {g}，j），j），使得$ν（j）= \ dim _ {\ dim _ {\ mathbb {c}}}}}}}}}}} \ mathfrak {g} = n $，我们称为$ in $ in $ in $ in n un n我们，我们在$ in n op n y y $ in y y y y y y我们in Che in Che in Che in Che in Che in Che in Che in Che in Che in Ape con y我们属于我们的; $（\ mathfrak {g}，j）$，满足$ν（j）= \ dim _ {\ mathbb {c}}} \ mathfrak {g} = n $，最大nilpotent（简短）的最大nilpotent（短）。讨论了尼尔曼群岛的代数维度，并讨论了左不变型MAXN复合结构的代数维度。此外，证明了对$（\ mathfrak {g}，j）$的结构定理，其中$ν（\ mathfrak {g}）= 3 $和$ j $是最大的复杂结构。
Let the pair $(\mathfrak{g},J)$ be a nilpotent Lie algebra $\mathfrak{g}$ (NLA for short) endowed with a nilpotent complex structure $J$. In this paper, motivated by a question in the work of Cordero, Fernández, Gray and Ugarte, we prove that $2\leq ν(J) \leq 3$ for $(\mathfrak{g},J)$ when $ν(\mathfrak{g})=2$, where $ν(\mathfrak{g})$ is the step of $\mathfrak{g}$ and $ν(J)$ is the unique smallest integer such that $\mathfrak{a}(J)_{ν(J)}=\mathfrak{g}$ as in Definition 1 and 8 of the paper by Cordero, Fernández, Gray and Ugarte. When $ν(\mathfrak{g})=3$, for arbitrary $n \geq 3$, there exists a pair $(\mathfrak{g},J)$ such that $ν(J)=\dim_{\mathbb{C}}\mathfrak{g}=n$, for which we call the $J$ in the pair $(\mathfrak{g},J)$, satisfying $ν(J)=\dim_{\mathbb{C}}\mathfrak{g}=n$, a maximal nilpotent (MaxN for short) complex structure. The algebraic dimension of a nilmanifold endowed with a left invariant MaxN complex structure is discussed. Furthermore, a structure theorem is proved for the pair $(\mathfrak{g},J)$, where $ν(\mathfrak{g})=3$ and $J$ is a MaxN complex structure.
