Maximal abelian C*-sublagebras of C*-algebras associated with self-similar maps and complex dynamical systems
Maximal abelian C*-sublagebras of C*-algebras associated with self-similar maps and complex dynamical systems
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与自相似映射和复杂动力系统相关的 C* 代数的最大阿贝尔 C* 子代数
DOI：
10.1016/j.jmaa.2017.06.044
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
T. Kajiwara and Y. Watatani
中科院分区：
文献类型：
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作者：
Masafumi Yoshino;廣川真男;Masafumi Yoshino;Masafumi Yoshino;Masafumi Yoshino;Masafumi Yoshino;Masafumi Yoshino;Masafumi Yoshino;吉野正史，田中 嘉成;吉野正史，山澤浩司;H. Kosaki;吉野正史，佐々木良勝;T. Kajiwara and Y. Watatani
我们考虑马尔可夫位移，复杂的动力系统和自相似映射之间的类比。它们的动力学分别由紧度量空间K上的0-1矩阵A、有理函数R和自相似映射γ给出。如果0-1矩阵A是不可约的且不是置换，则Cuntz-Krieger代数O A是单的且纯无限的。类似地，如果有理函数R被限制在Julia集JR上，自相似映射γ满足开集条件，则相应的CR-代数OR（JR）和O γ（K）是单的纯无限的.设A是0-1矩阵A的伴随无限路空间，则C（A）是A的极大交换子代数.本文证明了C（JR）是OR（JR）的极大交换子代数，C（K）是O γ（K）的极大交换子代数.
We consider an analogy among Markov shifts, complex dynamical systems and self-similar maps. Their dynamics are given by 0–1 matrices A, rational functions R and self-similar maps γ on a compact metric space K, respectively. If the 0–1 matrix A is irreducible and not a permutation, then the Cuntz–Krieger algebra O A is simple and purely infinite. Similarly, if the rational function R is restricted to the Julia set J R and the self-similar map γ satisfies the open set condition respectively, then the associated C⁎-algebras O R (J R) and O γ (K) are simple and purely infinite. Let Σ A be the associated infinite path space for the 0–1 matrix A, then C (Σ A) is known to be a maximal abelian subalgebra of O A. In this paper we shall show that C (J R) is a maximal abelian subalgebra of O R (J R) and C (K) is a maximal abelian subalgebra of O γ (K).