Maximal nilpotent complex structures
Maximal nilpotent complex structures
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最大幂零复合结构
DOI：
10.1007/s00031-021-09688-3
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发表时间：
2022
影响因子：
0.7
通讯作者：
Zheng Fangyang
中科院分区：
文献类型：
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作者：
Gao Qin;Zhao Quanting;Zheng Fangyang
设(𝔤，J)是赋有幂零复结构的幂零李代数𝔤(简称Nla)。本文受Cordero，Fernández，Gray和Ugarte[6]工作中的一个问题的启发，证明了2≤v(J)≤3当v(𝔤，J)=2时v(𝔤)=2时，其中v(𝔤)是𝔤的步长，v(J)是唯一的最小整数，使得𝔞(J)v(J)=𝔤如文[6，Def.1、8]。当v(𝔤)=3时，对任意n≥3，存在一个对(𝔤，J)使得v(J)=dimℂ𝔤=n，我们称它为对(𝔤，J)，满足v(J)=dimℂ𝔤=n，一个极大幂零(简称MaxN)复结构.讨论了具有左不变MaxN复结构的零流形的代数维数。进一步证明了(𝔤，J)对的一个结构定理，其中v(𝔤)=3，且J是MaxN复结构。
Let the pair (𝔤,J) be a nilpotent Lie algebra 𝔤 (NLA for short) endowed with a nilpotent complex structureJ. In this paper, motivated by a question in the work of Cordero, Fernández, Gray and Ugarte [6], we prove that 2 ≤v(J) ≤ 3 for (𝔤,J) whenv(𝔤) = 2, wherev(𝔤) is the step of 𝔤 andv(J) is the unique smallest integer such that 𝔞(J)v(J)= 𝔤 as in the [6, Def. 1, 8]. Whenv(𝔤) = 3, for arbitraryn≥ 3, there exists a pair (𝔤,J) such thatv(J) = dimℂ𝔤 =n, for which we call theJin the pair (𝔤,J), satisfyingv(J) = dimℂ𝔤 =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 (𝔤,J), wherev(𝔤) = 3 andJis a MaxN complex structure.