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

Authors

Adam C. Rennie, University of WollongongFollow
David I. Robertson, University of WollongongFollow
Aidan Sims, University of WollongongFollow

RIS ID

106890

Publication Details

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.

Abstract

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.

Grant Number

ARC/DP120100507

Additional Grant Number

http://purl.org/au-research/grants/ARC/DP120100507