Asymptotic Continuous Orbit Equivalence of Smale Spaces and Ruelle Algebras
Asymptotic Continuous Orbit Equivalence of Smale Spaces and Ruelle Algebras
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DOI：
10.4153/cjm-2018-012-x
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发表时间：
2017-03
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影响因子：
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通讯作者：
Kengo Matsumoto
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文献类型：
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作者：
Kengo Matsumoto
本文的第一部分引入Smale空间中的渐近连续轨道等价和渐近共轭的概念，并利用它们的对偶作用的渐近Ruelle代数刻画了它们。在第二部分中，我们从Smale空间引入了一个群胚$C^{\ast }$ -代数，它是渐近Ruelle代数的一个推广，并从Cuntz-Krieger代数的角度研究了推广的Ruelle代数。结果表明，渐近Ruelle代数在一定的圈作用下可实现为扩展Ruelle代数的不动点代数.
Abstract In the first part of the paper, we introduce notions of asymptotic continuous orbit equivalence and asymptotic conjugacy in Smale spaces and characterize them in terms of their asymptotic Ruelle algebras with their dual actions. In the second part, we introduce a groupoid $C^{\ast }$ -algebra that is an extended version of the asymptotic Ruelle algebra from a Smale space and study the extended Ruelle algebras from the view points of Cuntz–Krieger algebras. As a result, the asymptotic Ruelle algebra is realized as a fixed point algebra of the extended Ruelle algebra under certain circle action.