PROFINITE PRO-C-ALGEBRAS AND PRO-C-ALGEBRAS OF PROFINITE GROUPS

被引：0

作者：

El Harti, Rachid ^{[1
]}

Phillips, N. Christopher ^{[2
]}

Pinto, Paulo R. ^{[3
]}

机构：

[1] Univ Hassan I, Fac Sci & Tech, Dept Math & Comp Sci, Settat, Morocco

[2] Univ Oregon, Dept Math, Eugene, OR 97403 USA

[3] Univ Tecn Lisboa, Inst Super Tecn, Dept Math, P-1049001 Lisbon, Portugal

来源：

HOUSTON JOURNAL OF MATHEMATICS | 2014年 / 40卷 / 03期

基金：

美国国家科学基金会;

关键词：

Pro-C*-algebra; Profinite group; Profinite completion;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define the profinite completion of a C*-algebra, which is a pro-C*-algebra, as well as the pro-C*-algebra of a profinite group. We show that the continuous representations of the pro-C*-algebra of a profinite group correspond to the unitary representations of the group which factor through a finite group. We define natural homomorphisms from the C*-algebra of a locally compact group and its profinite completion to the pro-C*-algebra of the profinite completion of the group. We give some conditions for injectivity or surjectivity of these homomorphisms, but an important question remains open.

引用

页码：791 / 816

页数：26

共 18 条

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Bekka, MB
[J]. FORUM MATHEMATICUM, 1999, 11 (06) : 705 - 715
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[6] THE FULL CSTAR-ALGEBRA OF THE FREE GROUP ON 2 GENERATORS
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[10] MURPHY GJ, 1990, C ALGEBRAS OPERATOR

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PROFINITE PRO-C*-ALGEBRAS AND PRO-C*-ALGEBRAS OF PROFINITE GROUPS

PROFINITE PRO-C-ALGEBRAS AND PRO-C-ALGEBRAS OF PROFINITE GROUPS