Resumen de Boundary operator algebras for free uniform tree lattices

Guyan Robertson

• Let X be a finite connected graph, each of whose vertices has degree at least three. The fundamental group of X is a free group which acts on the boundary of the universal covering tree, endowed with a natural topology and Borel measure. The corresponding crossed product C*-algebra depends only on the rank of the free group and is a Cuntz-Krieger algebra whose structure is explicitly determined. The crossed product von Neumann algebra does not possess this rigidity. If the tree is homogeneous then the von Neumann algebra is a purely infinite hyperfinite factor whose exact type depends on whether X is bipartite or not.