Banach Journal of Mathematical Analysis

Limit dynamical systems and C-algebras from self-similar graph actions

Inhyeop Yi

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Abstract

In this article, we study dynamical and C-algebraic properties of self-similar group actions on finite directed graphs. We investigate the structure of limit dynamical systems induced from group actions on graphs, and we deduce conditions of group actions and graphs for the groupoid C-algebras defined by limit dynamical systems to be simple, separable, purely infinite, nuclear, and satisfying the universal coefficient theorem.

Article information

Source
Banach J. Math. Anal., Volume 11, Number 4 (2017), 764-784.

Dates
Received: 10 April 2016
Accepted: 28 October 2016
First available in Project Euclid: 22 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1498118444

Digital Object Identifier
doi:10.1215/17358787-2017-0016

Mathematical Reviews number (MathSciNet)
MR3708528

Zentralblatt MATH identifier
06841253

Subjects
Primary: 46L05: General theory of $C^*$-algebras 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20] 37D20: Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)

Keywords
self-similar graph action asymptotic equivalence limit dynamical system contracting regular G-transitive pseudofree groupoid groupoid $C^{*}$-algebra

Citation

Yi, Inhyeop. Limit dynamical systems and $C^{*}$ -algebras from self-similar graph actions. Banach J. Math. Anal. 11 (2017), no. 4, 764--784. doi:10.1215/17358787-2017-0016. https://projecteuclid.org/euclid.bjma/1498118444


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