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

TL;DR

This paper constructs and analyzes C*-algebras associated with Baumslag-Solitar groups using categories of paths, providing presentations, Morita equivalences, and K-theory computations for related algebras.

Contribution

It introduces a new approach using categories of paths to describe C*-algebras for Baumslag-Solitar groups, including generators, relations, and K-theory.

Findings

Complete description of Toeplitz algebras

K-theory computations for Cuntz-Kreiger algebras

Morita equivalence to crossed product C*-algebras

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.