Boundary Quotient C*-algebras of Products of Odometers

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 $\Q_\bN$ introduced by Cuntz are also investigated. As an easy consequence of our main results, it settles a boundary quotient C*-algebra constructed by Brownlowe-Ramagge-Robertson-Whittaker.

33 pages. Section 3 was cleaned up. Some minor changes were also made

References in corpus (4)

• C*-algebras associated to product systems of Hilbert bimodules
• On the K-theory of C*-algebras arising from integral dynamics
• Equilibrium states on right LCM semigroup C*-algebras
• Affine Actions and the Yang-Baxter Equation

Cited by in corpus (1)

• KMS States of Self-Similar $k$-Graph C*-Algebras