In this paper, we study deformations of complex structures on Lie algebras and its associated deformations of Dolbeault cohomology classes. A complete deformation of complex structures is constructed in a way similar to the Kuranishi family. The extension isomorphism is shown to be valid in this case. As an application, we prove that given a family of left-invariant deformations \(\{M_t\}_{t\in B}\) of a compact complex manifold \(M=(\Gamma \setminus G, J)\) where G is a Lie group, \(\Gamma\) a sublattice and J a left-invariant complex structure, the set of all \(t\in B\) such that the Dolbeault cohomology on \(M_t\) may be computed by left-invariant tensor fields is an analytic open subset of B.

在本文中，我们研究了李代数上复杂结构的变形及其相关的 Dolbeault 上同调类变形。复杂结构的完全变形以类似于仓西家族的方式构建。在这种情况下，扩展同构被证明是有效的。作为一个应用，我们证明给定一个紧复流形\(M=(\Gamma \setminus G, J)\ 的一系列左不变变形\(\{M_t\}_{t\in B}\ )\ )其中G是李群，\(\Gamma\)是子格，J是左不变复结构，所有\(t\in B\)的集合使得\(M_t\)上的 Dolbeault 上同调可以由左不变张量场计算，是B的解析开子集。