TY - JOUR
AU - Francesca Arici
AU - Adam Rennie
PY - 2019/10/19
Y2 - 2019/11/19
TI - The Cuntz-Pimsner extension and mapping cone exact sequences
JF - MATHEMATICA SCANDINAVICA
JA - MathScand
VL - 125
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-115634
UR - https://www.mscand.dk/article/view/115634
AB - 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.
ER -