The Cuntz-Pimsner extension and mapping cone exact sequences

• Francesca Arici ^[2] ; Adam Rennie ^[1]
  1. [1] University of Wollongong

     University of Wollongong

     Australia

     
  2. [2] Radboud University Nijmegen (Países Bajos)
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 125, Nº 2, 2019, págs. 291-319
• Idioma: inglés
• DOI: 10.7146/math.scand.a-115634
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• Resumen

  • For Cuntz-Pimsner algebras of bi-Hilbertian bimodules with finite Jones-Watatani index satisfying some side conditions, we give an explicit isomorphism between the K-theory exact sequences of the mapping cone of the inclusion of the coefficient algebra into a Cuntz-Pimsner algebra, and the Cuntz-Pimsner exact sequence. In the process we extend some results by the second author and collaborators from finite projective bimodules to certain finite index bimodules, and also clarify some aspects of Pimsner's `extension of scalars' construction.