Representations of finite groups and Cuntz-Krieger algebras

Abstract

We investigate the structure of the C*-algebras 𝒪ρ constructed by Doplicher and Roberts from the intertwining operators between the tensor powers of a representation ρ of a compact group. We show that each Doplicher-Roberts algebra is isomorphic to a corner in the Cuntz-Krieger algebra 𝒪A of a {0,1}-matrix A = Aρ associated to ρ. When the group is finite, we can then use Cuntz's calculation of the K-theory of 𝒪A to compute K*(𝒪ρ).