Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 383-399 |
| Number of pages | 17 |
| Journal | Journal of the Korean Mathematical Society |
| Volume | 57 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2020 |
Bibliographical note
Funding Information:Received January 30, 2019; Revised May 8, 2019; Accepted May 23, 2019. 2010 Mathematics Subject Classification. 37B10, 46L55, 37A55. Key words and phrases. Self-similar group, limit dynamical system, orbit equivalence. 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).
Publisher Copyright:
© 2020 Korean Mathematical Society.
Keywords
- And phrases
- Limit dynamical system
- Orbit equivalence
- Self-similar group