Guyan Robertson (Newcastle):
C*-algebras
associated with boundary actions on buildings
and their
K-theory
Let X be a finite connected graph. The fundamental group Γ of
X is a free group and acts on the universal covering tree Δ
and on its boundary ∂Δ. This boundary action may be
studied by means of the crossed product C*-algebra
C(∂Δ)
Γ.
The structure of this algebra can be explicitly determined. It is a
Cuntz-Krieger algebra.
Similar algebras may be defined for boundary actions on affine buildings
of dimension ≥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
K0 always has torsion.
This talk will outline some of the geometry
and algebra involved.