Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids
Flow equivalence and orbit equivalence for shifts of finite type and isomorphism of their groupoids
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有限型位移的流等价和轨道等价及其群形同构
DOI：
10.1016/j.jmaa.2018.09.056
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发表时间：
2016
影响因子：
1.3
通讯作者：
Gunnar Restorff
中科院分区：
文献类型：
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作者：
T. M. Carlsen;S. Eilers;E. Ortega;Gunnar Restorff
给出了单侧移位空间的连续轨道等价蕴含相关双边移位空间的流等价的条件。利用群胚技巧，我们证明了有限类型的移位总是这样的。这将松本和松井的一个结果从不可约推广到一般情况。证明了两个有限类型的单侧移位空间连续轨道等价的充要条件是它们的群胚是同构的，相应的双边移位是流等价的当且仅当它们是稳定同构的。作为应用，我们证明了两个无汇无源的有限有向图是移动等价的当且仅当对应的图C⁎-代数通过保对角同构稳定同构(当且仅当相应的Leavitt路代数通过保对角同构稳定同构)，以及两个拓扑马氏链是流等价的当且仅当对应的Cuntz-Krieger代数的稳定化之间存在保对角同构(后者将MatSumoto和Matui关于没有孤立点的不可约拓扑马尔可夫链的结果推广到关于一般拓扑马尔可夫链的结果)。我们还证明了对于一般的移位空间，强连续轨道等价蕴含着双边共轭。
We give conditions for when continuous orbit equivalence of one-sided shift spaces implies flow equivalence of the associated two-sided shift spaces. Using groupoid techniques, we prove that this is always the case for shifts of finite type. This generalises a result of Matsumoto and Matui from the irreducible to the general case. We also prove that a pair of one-sided shift spaces of finite type are continuously orbit equivalent if and only if their groupoids are isomorphic, and that the corresponding two-sided shifts are flow equivalent if and only if the groupoids are stably isomorphic. As applications we show that two finite directed graphs with no sinks and no sources are move equivalent if and only if the corresponding graph C⁎-algebras are stably isomorphic by a diagonal-preserving isomorphism (if and only if the corresponding Leavitt path algebras are stably isomorphic by a diagonal-preserving isomorphism), and that two topological Markov chains are flow equivalent if and only if there is a diagonal-preserving isomorphism between the stabilisations of the corresponding Cuntz–Krieger algebras (the latter generalises a result of Matsumoto and Matui about irreducible topological Markov chains with no isolated points to a result about general topological Markov chains). We also show that for general shift spaces, strongly continuous orbit equivalence implies two-sided conjugacy.
马尔可夫位移和 Cuntz-Krieger 代数的轨道等价
DOI：
--
发表时间：
2007
期刊：
影响因子：
--
作者：
Kengo;Matsumoto
通讯作者：
Matsumoto