AF vN代数中三角子代数的Lie理想

Lie Ideals in Triangular Subalgebras of AF Von Neumann Algebras

描述了AF von Neumann代数B中对角为Cartan子代数D的σ-弱闭三角子代数A的σ-弱闭Lie理想。证明了A中的σ-弱闭空间L是A的Lie理想当且仅当存在A的σ弱闭结合理想K和D的子空间Z使得K L K+Z。

We give a detailed description of the structure of a σ -weakly closed Lie ideal in a σ -weakly closed triangular subalgebra A of an AF von Neumann algebra B with Cartan subalgebra D. We prove that a σ - weakly closed subspace L of A is a Lie ideal in A if and only if there exists a closed associative ideal K of A and a σ -weakly closedsubspace Z of D such thatK lohtain in L lohtain in K-4-Z.