Subquotients of Hecke C*-algebras
Nathan Brownlowe, Nadia S. Larsen, Ian F. Putnam, Iain Raeburn
Abstract
The Bost-Connes Hecke C*-algebra can be regarded as a direct limit of subalgebras involving finite sets of primes. Each of these finite-prime analogues of the Bost-Connes algebra is a crossed product by a semigroup NF, where F is finite. We describe composition series of ideals for these semigroup crossed products in which the intermediate subquotients are finite direct sums of classifiable AT-algebras. We then use similar techniques to identify subquotients of the Bost-Connes algebra as classifiable AT-algebras.
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