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

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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


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


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