Banach Journal of Mathematical Analysis

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

Inhyeop Yi

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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

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

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

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Zentralblatt MATH identifier

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.)

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


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.

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