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
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 singlevertex $k$graph C*algebra
is simple.
To achieve this, one of our main steps is to construct a topological
$k$graph such that
its associated CuntzPimsner 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, ZappaSzép product
C*algebra, semigroup, odometer, topological $k$graph, product system, ZappaSzép product
