The Cuntz-Pimsner extension and mapping cone exact sequences
The Cuntz-Pimsner extension and mapping cone exact sequences
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 …