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ORBIT EQUIVALENCE ON SELF-SIMILAR GROUPS AND THEIR C-ALGEBRAS

  • Yi, Inhyeop (Department of Mathematics Education Ewha Womans University)
  • Received : 2019.01.30
  • Accepted : 2019.05.23
  • Published : 2020.03.01

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.

Keywords

References

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