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-P...
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| Published in: | Mathematica scandinavica Vol. 125; no. 2; pp. 291 - 319 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
19-10-2019
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| Online Access: | Get full text |
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| Summary: | 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. |
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| ISSN: | 0025-5521 1903-1807 |
| DOI: | 10.7146/math.scand.a-115634 |