Groupoid algebras as Cuntz-Pimsner algebras - Rennie, Adam; Robertson, David; Sims, Aidan (MATHEMATICA SCANDINAVICA, 2017)
We show that if G is a second countable locally compact Hausdorff étale groupoid carrying a suitable cocycle cG→Z, then the reduced C^*-algebra of G can be realised naturally as the Cuntz-Pimsner algebra of a correspondence over the reduced C^*-algebra of the kernel G_0 of c. If the full and reduced C^*-algebras of G_0 coincide, we deduce that the full and reduced C^*-algebras of G coincide. We obtain a six-term exact sequence describing the K-theory of C^*_r(G) in terms of that of C^*_r(G_0).