We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Mathematical Sciences

# Seminar Archives

"Let $X$ be a finite connected graph. The fundamental group $\Gamma$ of $X$ is a free group and acts on the universal covering tree $\Delta$ and on its boundary $\partial \Delta$. This boundary action may be studied by means of the crossed product $C^*$-algebra $C(\partial \Delta) \rtimes \Gamma$. The structure of this algebra can be explicitly determined. It is a {\it Cuntz-Krieger algebra}. Similar algebras may be defined for boundary actions on affine buildings of dimension $\ge 2$. These algebras have a structure analogous to that of a simple Cuntz-Krieger algebra and this is the motivation for a theory of higher rank Cuntz-Krieger algebras, which has been developed by T. Steger and G. Robertson. The K-theory of these algebras can be computed explicitly in some cases. Moreover, the class $[1]$ of the identity element in $K_0$ always has torsion. This talk will outline some of the geometry and algebra involved."