Boundary operator algebras for free uniform tree lattices

• Autores: Guyan Robertson
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 31, Nº 3, 2005, págs. 913-935
• Idioma: inglés
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• Resumen

  • 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.