The classification of some generalised Bunce-Deddens algebras

Abstract

We use $K$-theory to prove an isomorphism theorem for a large class of generalised Bunce-Deddens algebras constructed by Kribs and Solel from a directed graph $E$ and a sequence $\omega$ of positive integers. In particular, we compute the torsion-free component of the $K_0$-group for a class of generalised Bunce-Deddens algebras to show that supernatural numbers are a complete invariant for this class.

22 pages. v2: Updated research support statement and bibliography. This version accepted for publication in Journal of Functional Analysis

References in corpus (1)

• Inductive limit algebras from periodic weighted shifts on Fock space