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Symbolic dynamical systems and C*-algebrascontinuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Symbolic dynamical systems and C*-algebrasby Kengo Matsumoto.
Reminder of title:	continuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras /
Author:	Matsumoto, Kengo.
Published:	Singapore :Springer Nature Singapore :2025.
Description:	xiv, 359 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Symbolic dynamics.
Online resource:	https://doi.org/10.1007/978-981-97-9404-1
ISBN:	9789819794041$q(electronic bk.)

Symbolic dynamical systems and C*-algebrascontinuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras /
Matsumoto, Kengo.

Symbolic dynamical systems and C*-algebrascontinuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras /[electronic resource] :by Kengo Matsumoto. - Singapore :Springer Nature Singapore :2025. - xiv, 359 p. :ill., digital ;24 cm. - Mathematical physics studies,2352-3905. - Mathematical physics studies..

This book presents the interplay between topological Markov shifts and Cuntz-Krieger algebras by providing notations, techniques, and ideas in detail. The main goal of this book is to provide a detailed proof of a classification theorem for continuous orbit equivalence of one-sided topological Markov shifts. The continuous orbit equivalence of one-sided topological Markov shifts is classified in terms of several different mathematical objects: the étale groupoids, the actions of the continuous full groups on the Markov shifts, the algebraic type of continuous full groups, the Cuntz-Krieger algebras, and the K-theory dates of the Cuntz-Krieger algebras. This classification result shows that topological Markov shifts have deep connections with not only operator algebras but also groupoid theory, infinite non-amenable groups, group actions, graph theory, linear algebras, K-theory, and so on. By using this classification result, the complete classification of flow equivalence in two-sided topological Markov shifts is described in terms of Cuntz-Krieger algebras. The author will also study the relationship between the topological conjugacy of topological Markov shifts and the gauge actions of Cuntz-Krieger algebras.

ISBN: 9789819794041$q(electronic bk.)

Standard No.: 10.1007/978-981-97-9404-1doiSubjects--Topical Terms:

468098
Symbolic dynamics.

LC Class. No.: QA614.85

Dewey Class. No.: 514.74

Symbolic dynamical systems and C*-algebrascontinuous orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras /
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520 $a This book presents the interplay between topological Markov shifts and Cuntz-Krieger algebras by providing notations, techniques, and ideas in detail. The main goal of this book is to provide a detailed proof of a classification theorem for continuous orbit equivalence of one-sided topological Markov shifts. The continuous orbit equivalence of one-sided topological Markov shifts is classified in terms of several different mathematical objects: the étale groupoids, the actions of the continuous full groups on the Markov shifts, the algebraic type of continuous full groups, the Cuntz-Krieger algebras, and the K-theory dates of the Cuntz-Krieger algebras. This classification result shows that topological Markov shifts have deep connections with not only operator algebras but also groupoid theory, infinite non-amenable groups, group actions, graph theory, linear algebras, K-theory, and so on. By using this classification result, the complete classification of flow equivalence in two-sided topological Markov shifts is described in terms of Cuntz-Krieger algebras. The author will also study the relationship between the topological conjugacy of topological Markov shifts and the gauge actions of Cuntz-Krieger algebras.
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