中文摘要：

本文描述了AF C^＊-代数中闭Lie理想，证明了如果AF C^＊-代数A中的线性流形L是A的闭Lie理想，则存在A的闭结合理想I和A的典型masa D中的闭子代数研使得[A，I]^-属于L属于I＋E1，并且A中每一个这种形式的闭子空间都是A的闭Lie理想．

英文摘要：

We study Lie ideals in unital AF C^＊-algebras. It is shown that if a linear manifold L in an AF C^＊-algebra A is a closed Lie ideal in A, then there exists a closed associative ideal I and a closed subalgebra EI of the canonical masa D of A such that [A,I]^- belong to L belong to I ＋ EI, and that every closed subspace in this form is a closed Lie ideal in A.