## Abstract and Applied Analysis

### Asymptotic ${C}^{\ast }$-Algebras from ${\Bbb Z}^{k}$-Actions on Higher Rank Graphs

Inhyeop Yi

#### Abstract

For a dynamical system arising from ${\Bbb Z}^{k}$-action on a higher rank graph with finite vertex set, we show that the semidirect product of the asymptotic equivalence relation groupoid is essentially principal if and only if the $k$-graph satisfies the aperiodic condition. Then we show that the corresponding asymptotic Ruelle algebra is simple if the graph is primitive with the aperiodic condition.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 752497, 5 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393449619

Digital Object Identifier
doi:10.1155/2013/752497

Mathematical Reviews number (MathSciNet)
MR3068868

#### Citation

Yi, Inhyeop. Asymptotic ${C}^{\ast }$ -Algebras from ${\Bbb Z}^{k}$ -Actions on Higher Rank Graphs. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 752497, 5 pages. doi:10.1155/2013/752497. https://projecteuclid.org/euclid.aaa/1393449619

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