Subquotients of Hecke C^*-algebras

2003/09/26 by Nathan Brownlowe, Nadia S. Larsen, Brownlowe, Nathan +5
Mathematics · #46L55 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.math/0309429

18 pages

arxiv created 2003/09/26 · arxiv updated 2009/12/01

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 N^F, 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.

Related

• The ideal structure of the Hecke C*-algebra of Bost and Connes
• Bost-Connes systems, Hecke algebras, and induction
• Reconstructing the Bost--Connes semigroup actions from K-theory
• C^*-algebras associated with the ax+b-semigroup over \mathbb N
• Representations of Hecke algebras and dilations of semigroup crossed products