李代数Kuranishi形变族的收敛性
Convergence of the Kuranishi Deformation Family for Lie Algebras
DOI: 10.12677/pm.2025.152056, PDF,    科研立项经费支持
作者: 胡 严, 夏 炜：重庆理工大学理学院，重庆
关键词: 复结构；形变；Kuranishi族；幂级数法；Complex Structures； Deformations； Kuranishi Family； Power Series Methods
摘要: Kuranishi形变族是复流形形变理论中一个重要的研究对象。在李代数上复结构的形变理论中，相应的Kuranishi形变族也是存在的，其构造方式与复流形的情况类似。本文的目标是借鉴Liu-Rao-Yang的方法为李代数上Kuranishi形变族的收敛性提供一个新的证明。
Abstract: Kuranishi deformation family is an important subject in the deformation theory of complex manifolds. In the deformation theory of complex structures on Lie algebras, the corresponding Kuranishi deformation family also exists, and their construction methods are similar to those in the case of complex manifolds. The goal of this paper is to provide a new proof for the convergence of Kuranishi deformation family on Lie algebras by drawing on the method of Liu-Rao-Yang.
文章引用：胡严, 夏炜. 李代数Kuranishi形变族的收敛性[J]. 理论数学, 2025, 15(2): 147-152. https://doi.org/10.12677/pm.2025.152056

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