J. Korean Math. Soc. 2020; 57(2): 383-399
Online first article July 17, 2019 Printed March 1, 2020
https://doi.org/10.4134/JKMS.j190090
Copyright © The Korean Mathematical Society.
Inhyeop Yi
Ewha Womans University
Following Matsumoto's definition of continuous orbit equivalence for one-sided subshifts of finite type, we introduce the notion of orbit equivalence to canonically associated dynamical systems, called the limit dynamical systems, of self-similar groups. We show that the limit dynamical systems of two self-similar groups are orbit equivalent if and only if their associated Deaconu groupoids are isomorphic as topological groupoids. We also show that the equivalence class of Cuntz-Pimsner groupoids and the stably isomorphism class of Cuntz-Pimsner algebras of self-similar groups are invariants for orbit equivalence of limit dynamical systems.
Keywords: Self-similar group, limit dynamical system, orbit equivalence
MSC numbers: 37B10, 46L55, 37A55
Supported by: This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1B07048313).
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