The extension class and KMS states for Cuntz--Pimsner algebras of some bi-Hilbertian bimodules

@article{Rennie2015TheEC,
  title={The extension class and KMS states for Cuntz--Pimsner algebras of some bi-Hilbertian bimodules},
  author={Adam Graham Rennie and David Robertson and Aidan Sims},
  journal={arXiv: K-Theory and Homology},
  year={2015}
}
For bi-Hilbertian $A$-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 $C^*$-module version of the Jones index for bi-Hilbertian bimodules. The Jones index data also determines a novel quasi-free dynamics and KMS states on these Cuntz--Pimsner algebras. 

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