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

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

2011-11-29

arxiv.org/abs/1111.6927v2

Mathematics

Operator Algebras

Fixed a gap in the proof that the groups are quasi-lattice ordered, including a larger discussion of the topic

Scientific paper

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.

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