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Boundary operator algebras for free uniform tree Lattices

Lookup NU author(s): Professor Guyan Robertson


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Let X be a finite connected graph, each of whose vertices has degree at least three. The fundamental group Γ of X is a free group and acts on the universal covering tree Δ and on its boundary ∂Δ, endowed with a natural topology and Borel measure. The crossed product C*-algebra C(∂Δ) ⋊ Γ depends only on the rank of Γ and is a Cuntz-Krieger algebra whose structure is explicitly determined. The crossed product von Neumann algebra does not possess this rigidity. If X is homogeneous of degree q + 1 then the von Neumann algebra L∞ (∂Δ) ⋊ Γ is the hyperfinite factor of type IIIλ where λ = 1/q2 if X is bipartite, and λ = 1/q otherwise. © 2005 University of Houston.

Publication metadata

Author(s): Robertson G

Publication type: Article

Publication status: Published

Journal: Houston Journal of Mathematics

Year: 2005

Volume: 31

Issue: 3

Pages: 913-935

Print publication date: 01/01/2005

ISSN (print): 0362-1588

ISSN (electronic):

Publisher: University of Houston



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