Orbit equivalence on self-similar groups and their C*-algebras

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 languageEnglish
Pages (from-to)383-399
Number of pages17
JournalJournal of the Korean Mathematical Society
Issue number2
StatePublished - 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.


  • And phrases
  • Limit dynamical system
  • Orbit equivalence
  • Self-similar group


Dive into the research topics of 'Orbit equivalence on self-similar groups and their C*-algebras'. Together they form a unique fingerprint.

Cite this