C*-algebras for categories of paths associated to the Baumslag-Solitar groups

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Abstract

In this paper, we describe the C*-algebras associated to the Baumslag-Solitar groups with the ordering defined by the usual presentations. These are Morita equivalent to the crossed product C*-algebras obtained by letting the group act on its directed boundary. We use the method of categories of paths to define the algebras, and to deduce the presentation by generators and relations. We obtain a complete description of the Toeplitz algebras, and we compute the K-theory of the Cuntz-Kreiger algebras.

Original languageEnglish (US)
Pages (from-to)728-754
Number of pages27
JournalJournal of the London Mathematical Society
Volume86
Issue number3
DOIs
StatePublished - Dec 2012

ASJC Scopus subject areas

  • Mathematics(all)

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