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

Title
ORBIT EQUIVALENCE ON SELF-SIMILAR GROUPS AND THEIR C*-ALGEBRAS
Authors
Yi, Inhyeop
Ewha Authors
이인협
SCOPUS Author ID
이인협scopus
Issue Date
2020
Journal Title
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
ISSN
0304-9914JCR Link

2234-3008JCR Link
Citation
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY vol. 57, no. 2, pp. 383 - 399
Keywords
Self-similar grouplimit dynamical systemorbit equivalence
Publisher
KOREAN MATHEMATICAL SOC
Indexed
SCIE; SCOPUS; KCI WOS
Document Type
Article
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.
DOI
10.4134/JKMS.j190090
Appears in Collections:
사범대학 > 수학교육과 > Journal papers
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