某些双模的Cuntz—Pimsner代数的扩展类和KMS态

arXiv: K-Theory and Homology Pub Date : 2015-01-22 DOI:10.1142/S1793525317500108

A. Rennie, D. Robertson, A. Sims

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引用次数: 25

摘要

对于bi-Hilbertian $A$-双模，在Kajiwara- Pinzari- Watatani的意义上，我们构造了一个Kasparov模，表示定义了Cuntz- Pimsner代数的扩展类。该构造利用了一个奇异期望，该期望是使用双希尔伯特双模的琼斯指数的$C^*$-模版本定义的。Jones指数数据还确定了Cuntz- Pimsner代数上的一种新的准自由动力学和KMS态。

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

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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arXiv: K-Theory and Homology

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