投射有限pro-C*-代数与投射有限群的pro-C*-代数
算子代数
2012-04-23 v2
摘要
我们定义了C*-代数的投射有限完备化（它是一个pro-C*-代数），以及投射有限群的pro-C*-代数。我们证明了投射有限群的pro-C*-代数的连续表示对应于该群的通过有限群分解的酉表示。我们定义了局部紧群的C*-代数及其投射有限完备化到该群投射有限完备化的pro-C*-代数的自然同态。我们给出了这些同态为单射或满射的一些条件，但一个重要问题仍然悬而未决。
引用
@article{arxiv.1110.3411,
title = {Profinite pro-C*-algebras and pro-C*-algebras of profinite groups},
author = {Rachid El Harti and N. Christopher Phillips and Paulo R. Pinto},
journal= {arXiv preprint arXiv:1110.3411},
year = {2012}
}
备注
18 pages; no figures. Changes from the previous version: Questions 3.14 and 3.15 in the previous version have been answered. In this version, see Corollary 3.14, Proposition 3.16, and Examples 3.17 and 3.18. Some related changes have been made elsewhere. Some local reorganization has been done, and some misprints corrected. Houston J. Math., to appear