Groupoid algebras as Cuntz: Pimsner algebras

• Adam Rennie ^[1] ; David Robertson ^[1] ; Aidan Sims ^[1]
  1. [1] University of Wollongong-AUSTRALIA
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 120, Nº 1, 2017, págs. 115-123
• Idioma: inglés
• DOI: 10.7146/math.scand.a-25507
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• Resumen

  • 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).