English

Boundary $C^*$-algebras of triangle geometries

Operator Algebras 2014-07-29 v1 Group Theory K-Theory and Homology

Abstract

Let Δ\Delta be a building of type A~2\widetilde A_2 and order qq, with maximal boundary Ω\Omega. Let Γ\Gamma be a group of type preserving automorphisms of Δ\Delta which acts regularly on the chambers of Δ\Delta. Then the crossed product CC^*-algebra C(Ω)ΓC(\Omega) \rtimes \Gamma is isomorphic to M3(q+1)\clOq2\clOq2M_{3(q+1)} \otimes\cl O_{q^2}\otimes\cl O_{q^2}, where \clOn\cl O_n denotes the Cuntz algebra generated by nn isometries whose range projections sum to the identity operator.

Keywords

Cite

@article{arxiv.1308.0908,
  title  = {Boundary $C^*$-algebras of triangle geometries},
  author = {Guyan Robertson},
  journal= {arXiv preprint arXiv:1308.0908},
  year   = {2014}
}