CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Boundary quotient C*-algebras of products of odometers

  • Hui Li,
    Department of Mathematics and Statistics, University of Windsor, Windsor ON N9B 3P4
  • Dilian Yang,
    Department of Mathematics and Statistics, University of Windsor, Windsor ON N9B 3P4
Format:   LaTeX   MathJax   PDF  

Abstract

In this paper, we study the boundary quotient C*-algebras associated to products of odometers. One of our main results shows that the boundary quotient C*-algebra of the standard product of $k$ odometers over $n_i$-letter alphabets ($1\le i\le k$) is always nuclear, and that it is a UCT Kirchberg algebra if and only if $\{\ln n_i: 1\le i\le k\}$ is rationally independent, if and only if the associated single-vertex $k$-graph C*-algebra is simple. To achieve this, one of our main steps is to construct a topological $k$-graph such that its associated Cuntz-Pimsner C*-algebra is isomorphic to the boundary quotient C*-algebra. Some relations between the boundary quotient C*-algebra and the C*-algebra $\mathrm{Q}_\mathbb{N}$ introduced by Cuntz are also investigated.
Keywords: C*-algebra, semigroup, odometer, topological $k$-graph, product system, Zappa-Szép product C*-algebra, semigroup, odometer, topological $k$-graph, product system, Zappa-Szép product
MSC Classifications: 46L05 show english descriptions General theory of $C^*$-algebras 46L05 - General theory of $C^*$-algebras
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/