The extension class and KMS states for Cuntz–Pimsner algebras of some bi-Hilbertian bimodules
The extension class and KMS states for Cuntz–Pimsner algebras of some bi-Hilbertian bimodules
For bi-Hilbertian [Formula: see text]-bimodules, in the sense of Kajiwara–Pinzari–Watatani, we construct a Kasparov module representing the extension class defining the Cuntz–Pimsner algebra. The construction utilises a singular expectation which is defined using the [Formula: see text]-module version of the Jones index for bi-Hilbertian bimodules. The Jones index data also …