30 research outputs found
C*-algebras for categories of paths asociated to the Baumslag-Solitar groups
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.Comment: To appear in the Journal of the London Mathematical Societ
Relative graphs and pullbacks of relative Toeplitz graph algebras
In this note we generalize a result from a recent paper of Hajac, Reznikoff
and Tobolski (2020). In that paper they give conditions they call admissibility
on a pushout diagram in the category of directed graphs implying that the
-algebras of the graphs form a pullback diagram. We consider a larger
category of relative graphs that correspond to relative Toeplitz graph
algebras. In this setting we give necessary and sufficient conditions on the
pushout to get a pullback of -algebras.Comment: 14 pages, 7 figure