Symbolic Dynamical Systems and C*-Algebras

Continuous Orbit Equivalence of Topological Markov Shifts and Cuntz–Krieger Algebras

Kengo Matsumoto (Autor)

Buch | Hardcover

359 Seiten

2025 | 2025 ed.
Springer Verlag, Singapore
978-981-97-9403-4 (ISBN)

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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.

Kengo Matsumoto is currently Professor at Joetsu University of Education.

Introduction.- Topological Markov Shifts.- Flow Equivalence.- Continuous Orbit Equivalence.- Etale Groupoids and Cuntz–Krieger Algebras.- K-Theory for Inﬁnite Simple 𝑪∗-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.

Erscheinungsdatum	15.05.2025
Reihe/Serie	Mathematical Physics Studies
Zusatzinfo	5 Illustrations, black and white
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie
Schlagworte	C*-algebra • Continuous Orbit Equivalence • Cuntz-Krieger Algebra • Etale Groupoid • Flow Equivalence • K-theory • Symbolic Dynamical System • Topological Markov Shift
ISBN-10	981-97-9403-X / 981979403X
ISBN-13	978-981-97-9403-4 / 9789819794034
Zustand	Neuware