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Subquotients of Hecke C*-algebras

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journal contribution
posted on 2025-05-09, 05:53 authored by Nathan Brownlowe, N. S. Larsen, I. F. Putnam, Iain Raeburn
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 vertical bar S vertical bar = 1, these actions are odometers and the crossed products are Bunce-Deddens algebras; when vertical bar S vertical bar > 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.

History

Journal title

Ergodic Theory and Dynamical Systems

Volume

25

Pagination

1503-1520

Article number

5

Publisher

Cambridge University Press

Language

  • en, English

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