State splitting, strong shift equivalence and stable isomorphism of Cuntz-Krieger algebras
State splitting, strong shift equivalence and stable isomorphism of Cuntz-Krieger algebras
复制标题
Cuntz-Krieger代数的状态分裂、强移位等价性和稳定同构
DOI：
10.1080/14689367.2018.1470227
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Kengo Matsumoto
中科院分区：
文献类型：
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作者：
Kengo Matsumoto
我们证明，如果两个非负矩阵是强移位等价的，则具有广义规范作用的相关稳定 Cuntz-Krieger 代数是共轭的。证明是通过纯函数解析方法完成的，基于通过强移位等效矩阵从二部有向图构造非原性双模，从而可以阐明相关稳定Cuntz-Krieger代数之间稳定同构的K理论行为。我们还检查了通过状态分裂图获得的矩阵的机制，以便根据 Cuntz-Krieger 代数与规范 masas 和无稳定性规范作用的某些等价关系来描述拓扑马尔可夫位移的拓扑共轭。
We prove that if two nonnegative matrices are strong shift equivalent, the associated stable Cuntz–Krieger algebras with generalized gauge actions are conjugate. The proof is done by a purely functional analytic method and based on constructing imprimitivity bimodule from bipartite directed graphs through strong shift equivalent matrices, so that we may clarifyK-theoretic behaviour of the stable isomorphism between the associated stable Cuntz–Krieger algebras. We also examine our machinery for the matrices obtained by state splitting graphs, so that topological conjugacy of the topological Markov shifts is described in terms of some equivalence relation of the Cuntz–Krieger algebras with canonical masas and the gauge actions without stabilization.