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arXiv · 1501.05363

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

Adam Rennie·David Robertson·Aidan Sims
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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.

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Adam Rennie, David Robertson, Aidan Sims. 2016-03-02. The extension class and KMS states for Cuntz--Pimsner algebras of some bi-Hilbertian bimodules. https://arxiv.org/abs/1501.05363

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