## Banach Journal of Mathematical Analysis

### Limit dynamical systems and $C^{*}$-algebras from self-similar graph actions

Inhyeop Yi

#### 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
Accepted: 28 October 2016
First available in Project Euclid: 22 June 2017

https://projecteuclid.org/euclid.bjma/1498118444

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

Mathematical Reviews number (MathSciNet)
MR3708528

Zentralblatt MATH identifier
06841253

#### 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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