Groups with faithful irreducible projective unitary representations

被引：1

作者：

Bekka, Bachir ^{[1
]}

de la Harpe, Pierre ^{[2
]}

机构：

[1] Univ Rennes 1, IRMAR, CNRS, UMR 6625, F-35042 Rennes, France

[2] Univ Geneva, Sect Math, CH-1211 Geneva 4, Switzerland

来源：

FORUM MATHEMATICUM | 2013年 / 25卷 / 03期

基金：

瑞士国家科学基金会;

关键词：

Projective unitary representations; irreducible representations; projectively faithful representations; central extensions; stem covers; capable groups; EXTENSIONS;

D O I：

10.1515/FORM.2011.126

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a countable group Gamma and a multiplier zeta is an element of Z(2)(Gamma,T), we study the property of Gamma having a unitary projective zeta-representation which is both irreducible and projectively faithful. We show that this property is equivalent to Gamma being the quotient of an appropriate group by its centre. Moreover, we give a criterion in terms of the minisocle of Gamma. Several examples are described to show the existence of various behaviours.

引用

页码：505 / 531

页数：27

共 50 条

[1] FAITHFUL IRREDUCIBLE PROJECTIVE REPRESENTATIONS OF METABELIAN GROUPS
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[J]. JOURNAL OF ALGEBRA, 1976, 38 (01) : 8 - 28
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[6] IRREDUCIBLE REPRESENTATIONS OF UNITARY AND LORENTZ GROUPS
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