Resumen de Groupoid algebras as Cuntz: Pimsner algebras

Adam Rennie, David Robertson, Aidan Sims

• We show that if G is a second countable locally compact Hausdorff étale groupoid carrying a suitable cocycle c:G→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 G0 of c. If the full and reduced C∗-algebras of G0 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(G0).