ORBIT EQUIVALENCE ON SELF-SIMILAR GROUPS AND THEIR C*-ALGEBRAS
- 주제(키워드) Self-similar group , limit dynamical system , orbit equivalence
- 주제(기타) Mathematics, Applied
- 주제(기타) Mathematics
- 설명문(일반) [Yi, Inhyeop] Ewha Womans Univ, Dept Math Educ, Seoul 03760, South Korea
- 등재 SCIE, SCOPUS, KCI등재
- 발행기관 KOREAN MATHEMATICAL SOC
- 발행년도 2020
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000168823
- 본문언어 영어
- Published As https://dx.doi.org/10.4134/JKMS.j190090
- 저작권 이화여자대학교 논문은 저작권에 의해 보호받습니다.
초록/요약
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.
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