Skip to main content
placeholder image

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

Journal Article


Download full-text (Open Access)

Abstract


  • For bi-Hilbertian (Formula presented.)-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 presented.)-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.

Publication Date


  • 2017

Citation


  • Rennie, A., Robertson, D. & Sims, A. (2017). The extension class and KMS states for Cuntz–Pimsner algebras of some bi-Hilbertian bimodules. Journal of Topology and Analysis, 9 (2), 297-327.

Scopus Eid


  • 2-s2.0-84963657377

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7167&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6137

Number Of Pages


  • 30

Start Page


  • 297

End Page


  • 327

Volume


  • 9

Issue


  • 2

Abstract


  • For bi-Hilbertian (Formula presented.)-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 presented.)-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.

Publication Date


  • 2017

Citation


  • Rennie, A., Robertson, D. & Sims, A. (2017). The extension class and KMS states for Cuntz–Pimsner algebras of some bi-Hilbertian bimodules. Journal of Topology and Analysis, 9 (2), 297-327.

Scopus Eid


  • 2-s2.0-84963657377

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7167&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6137

Number Of Pages


  • 30

Start Page


  • 297

End Page


  • 327

Volume


  • 9

Issue


  • 2