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http://dx.doi.org/10.4134/JKMS.j190090

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

Yi, Inhyeop (Department of Mathematics Education Ewha Womans University)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.2, 2020 , pp. 383-399 More about this Journal
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
Self-similar group; limit dynamical system; orbit equivalence;
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