Boundary 𝐶*-algebras for acylindrical groups

Abstract

Abstract. Let ∆ be an infinite, locally finite tree with more than two ends. Let Γ < Aut(∆) be an acylindrical uniform lattice. Then the boundary algebra A Γ = C(∂∆) Γ is a simple Cuntz-Krieger algebra whose K-theory is determined explicitly.

Invariant boundary distributions for finite graphs

“…Suppose that each vertex of G has at least three neighbours. Then the compact space ∂Δ is perfect (hence uncountable) and A = C(∂Δ) Γ is a Cuntz-Krieger algebra [4,5]. This coefficient is zero, since α ∈ ker(T − I ).…”

C⁎-algebras associated to graphs of groups

“…This construction is a special case of the graphs of groups considered in, for example, [5]. The C * -algebra construction is a special case of results of [40,43,35].…”