Symbolic Dynamical Systems and C*-Algebras : Continuous Orbit Equivalence of Topological Markov Shifts and Cuntz-Krieger Algebras (Mathematical Physics Studies)

Matsumoto, Kengo

Springer Verlag, Singapore（2026/02発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 359 p.
• 言語 ENG
• 商品コード 9789819794065

Full Description

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.

Contents

Introduction.- Topological Markov Shifts.- Flow Equivalence.- Continuous Orbit Equivalence.- Etale Groupoids and Cuntz-Krieger Algebras.- K-Theory for Infinite Simple 푪∗-Algebras.- K-Theory for Cuntz-Krieger Algebras.- Strong Shift Equivalence, Flow Equivalence and Cuntz-Krieger Algebras.- Classification Theorem for Continuous Orbit Equivalence.- Gauge Actions and Continuous Orbit Equivalence.- Classification Theorem for Flow Equivalence and Topological Conjugacy.