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

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.

To appear in the Journal of the London Mathematical Society

References in corpus (2)

• A class of $C^{\ast }$-algebras generalizing both graph algebras and homeomorphism $C^{\ast }$-algebras IV, pure infiniteness
• Groupoids and C*-algebras for categories of paths

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