Boundary Quotient C^* -algebras of Products of Odometers. (7th January 2019) - Li, Hui; Yang, Dilian
Abstract: In this paper, we study the boundary quotient C^* -algebras associated with 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 (1ik) is always nuclear, and that it is a UCT Kirchberg algebra if and only if {n_i:1ik} 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_N introduced by Cuntz are also investigated.