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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: "C*-algebras associated with boundary actions on buildings and their K-theory"

Presented by Guyan Robertson (Newcastle),

22 November 2004 16:00 in CM221

"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."

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