Lie Ideals in AF C~*-Algebras  

AF C~*-代数中的Lie理想(英文)

作　　者：纪培胜[1] 王琳[1] 

机构地区：[1]青岛大学数学系,山东青岛266071

出　　处：《Journal of Mathematical Research and Exposition》2005年第4期589-592,共4页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China (10371016)

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.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EI使得[A,I](?)L(?)I+EI,并且A中每一个这种形式的闭子空间都是A的闭Lie理想.

关 键 词：AF C^＊-algebra Lie ideal canonical masa. 

分 类 号：O177.5[理学—数学]