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

被引：12

作者：

Rennie, Adam ^{[1
]}

Robertson, David ^{[1
]}

Sims, Aidan ^{[1
]}

机构：

[1] Univ Wollongong, Sch Math & Appl Stat, Northfields Ave 2522, Wollongong, NSW 2522, Australia

来源：

JOURNAL OF TOPOLOGY AND ANALYSIS | 2017年 / 9卷 / 02期

基金：

澳大利亚研究理事会;

关键词：

Kasparov module; extension; Cuntz-Pimsner algebra; KMS state; C-ASTERISK-ALGEBRAS; NONCOMMUTATIVE GEOMETRY; CROSSED-PRODUCTS; GRAPH ALGEBRAS; ENDOMORPHISMS; SIMPLICITY;

D O I：

10.1142/S1793525317500108

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：297 / 327

页数：31

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