Subquotients of Hecke C*-algebras

Authors

Nathan Brownlowe, University of WollongongFollow
Nadia Larsen, University of Copenhagen
Ian Putnam, University of Victoria
Iain Raeburn, University of NewcastleFollow

RIS ID

18845

Publication Details

Brownlowe, N., Larsen, N. S., Putnam, I. F. & Raeburn, I. (2005). Subquotients of Hecke C*-algebras. Ergodic Theory and Dynamical Systems, 25 (5), 1503-1520.

Abstract

We realize the Hecke C^*-algebra C_Q of Bost and Connes as a direct limit of Hecke C^*-algebras which are semigroup crossed products by N^F, for F a finite set of primes. For each approximating Hecke C^*-algebra we describe a composition series of ideals. In all cases there is a large type I ideal and a commutative quotient, and the intermediate subquotients are direct sums of simple C^*-algebras. We can describe the simple summands as ordinary crossed products by actions of Z^S for S a finite set of primes. When |S|=1, these actions are odometers and the crossed products are Bunce–Deddens algebras; when |S|>1, the actions are an apparently new class of higher-rank odometer actions, and the crossed products are an apparently new class of classifiable AT-algebras.