The K-theory of the C*-algebras of 2-rank graphs associated to complete bipartite graphs

Abstract

Using a result of Vdovina, we may associate to each complete connected bipartite graph $\kappa$ a $2$-dimensional square complex, which we call a tile complex, whose link at each vertex is $\kappa$. We regard the tile complex in two different ways, each having a different structure as a $2$-rank graph. To each $2$-rank graph is associated a universal C*-algebra, for which we compute the K-theory, thus providing a new infinite collection of $2$-rank graph algebras with explicit K-groups. We determine the homology of the tile complexes, and give generalisations of the procedures to complexes and systems consisting of polygons with a higher number of sides.

24 pages, 9 figures. Revised 2020/10/05. Section 4 and Figure 8 added Revised 2021/02/17. New figure (7) added. Changes made for clarity

References in corpus (3)

• Higher rank graph C*-algebras
• On the K-theory of higher rank graph C*-algebras
• Groups acting on products of trees, tiling systems and analytic K-theory