中文摘要：

本文给出因子von Neumann代数中的幂等算子在广义Lie积下的一个刻画；得到因子von Neumann代数中套子代数的幂等算子在Lie积下的一个特征．作为应用，研究了因子von Neumann代数中套子代数上的Lie同构，并证明因子von Neumann代数中套子代数之间的Lie同构，要么是同构与广义迹之和，要么是负反同构与广义迹之和．

英文摘要：

In this paper, idempotents of factor von Neumann algebras is characterized by general Lie product; a characterization of idempotents of nest subalgebras in factor von Neumann algebras is obtained by Lie product. As its application, Lie isomorphisms of nest subalgebras in factor von Neumann algebras are studied, and it is shown that every Lie isomorphism between two nest subalgebras of a factor von Neumann algebra is either the sum of an isomorphism and a general trace or the sum of a negative anti-isomorphism and a general trace.