Boundary C~*-algebras of triangle geometries

摘要

Let Δ be a building of type A_2 and order q, with maximal boundary Ω. Let Γ be a group of type preserving automorphisms of Δ which acts regularly on the chambers of Δ. Then the crossed product C~* -algebra C(Ω) × Γ is isomorphic to M_(3(q+1)) ? O_(q2) ? O_(q2), where O_n denotes the Guntz algebra generated by n isometries whose range projections sum to the identity operator.