希尔伯特双模交叉积的Cuntz-Krieger唯一性定理
算子代数
2015-01-30 v5 动力系统
泛函分析
摘要
我们证明，由希尔伯特双模X的任意忠实协变表示生成的C*-代数典范同构于与X相关的交叉积，前提是Rieffel的诱导表示函子X-ind是拓扑自由的。我们讨论了这一结果如何应用于由带有圆规约作用的生成关系所定义的泛C*-代数。特别地，它导致了各种交叉积同构定理的推广，并且被证明等价于有限图C*-代数的Cuntz-Krieger唯一性定理（在此过程中，发现了Cuntz-Krieger代数作为Exel相互作用交叉积的一个有趣实现）。
引用
@article{arxiv.1010.0446,
title = {Cuntz-Krieger uniqueness theorem for crossed products by Hilbert bimodules},
author = {B. K. Kwasniewski},
journal= {arXiv preprint arXiv:1010.0446},
year = {2015}
}
备注
This paper has been withdrawn by the author. The results of the paper are presented in a more accurate and extended form in the following published papers: Topological freeness for Hilbert bimodules (arXiv:1212.0361), Crossed products for interactions and graph algebras (arXiv:1301.5125), Ideal structure of crossed products by endomorphisms via reversible extensions of C*-dynamical systems (arXiv:1404.4928)