Ideals of the core of C*-algebras associated with self-similar maps
Ideals of the core of C*-algebras associated with self-similar maps
复制标题
DOI：
10.7900/jot.2015feb23.2069
复制
发表时间：
2013-06
期刊：
影响因子：
--
通讯作者：
Tsuyoshi Kajiwara;Y. Watatani
中科院分区：
文献类型：
--
作者：
Tsuyoshi Kajiwara;Y. Watatani
我们给出了一定条件下与自相似映射相关的C*代数核心理想的完整分类。任何理想完全由与自相似集K的系数代数C(K)的交来确定。K的相应闭子集由自相似映射的奇点结构来描述。特别是，当且仅当自相似映射没有分支点时，核心是简单的。核心的矩阵表示本质上用于证明分类。
We give a complete classification of the ideals of the core of the C*-algebras associated with self-similar maps under a certain condition. Any ideal is completely determined by the intersection with the coefficient algebra C(K) of the self-similar set K. The corresponding closed subset of K is described by the singularity structure of the self-similar map. In particular the core is simple if and only if the self-similar map has no branch point. A matrix representation of the core is essentially used to prove the classification.