Nonnuclear Bunce-Deddens algebras
arXiv:2607.28597
The paper defines and studies nonnuclear Bunce-Deddens C*-algebras built from free odometer actions of certain nonamenable groups, showing they have regularity properties and computing their K-theory.
Abstract
We introduce nonnuclear Bunce-Deddens algebras, defined as reduced crossed product C*-algebras associated with free odometer actions of nonamenable countable discrete residually finite groups on a Cantor space. These are nonnuclear counterparts to the generalised Bunce-Deddens algebras introduced by Orfanos. For large classes of groups, we show that they share many regularity properties, including real rank zero, stable rank one, strict comparison of positive elements, and admitting a unique tracial state. In many cases, we deduce that they are even selfless and hence pure. Finally, we compute the K-theory of Bunce-Deddens algebras over nonabelian free groups.
16 pages, 1 figure. Comments welcome