Exactness of locally compact groups

被引：18

作者：

Brodzki, Jacek ^{[1
]}

Cave, Chris ^{[2
]}

Li, Kang ^{[2
]}

机构：

[1] Univ Southampton, Sch Math, Southampton SO17 1BJ, Hants, England

[2] Univ Copenhagen, Dept Math Sci, Univ Pk 5, DK-2100 Copenhagen O, Denmark

来源：

ADVANCES IN MATHEMATICS | 2017年 / 312卷

基金：

英国工程与自然科学研究理事会; 新加坡国家研究基金会;

关键词：

Exactness of groups; Amenable actions; Coarse geometry; CONNES CONJECTURE; AMENABILITY; ALGEBRAS; PROPERTY; SYSTEMS; SPACES;

D O I：

10.1016/j.aim.2017.03.020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give some new characterizations of exactness for locally compact second countable groups. In particular, we prove that a locally compact second countable group is exact if and only if it admits a topologically amenable action on a compact Hausdorff space. This answers an open question by Anantharaman-Delaroche. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：209 / 233

页数：25

共 50 条

[1] The approximation property and exactness of locally compact groups
Suzuki, Yuhei
[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2021, 73 (01) : 263 - 275
[2] EXACTNESS FOR EQUATIONALLY COMPACT GROUPS
GARAVAGLIA, S
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (03): : A391 - A391
[3] A THEORY OF DISTRIBUTIONS FOR LOCALLY COMPACT ABELIAN GROUPS AND COMPACT GROUPS
REID, GA
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1966, 16 : 415 - &
[4] The structure of homomorphisms of connected locally compact groups into compact groups
Shtern, A. I.
[J]. IZVESTIYA MATHEMATICS, 2011, 75 (06) : 1279 - 1304
[5] THE STRUCTURE OF LOCALLY COMPACT GROUPS
GLEASON, AM
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1954, 60 (05) : 461 - 463
[6] Locally compact sofic groups
Bowen, Lewis
Burton, Peter
[J]. ISRAEL JOURNAL OF MATHEMATICS, 2022, 251 (01) : 239 - 270
[7] SUBGROUPS OF LOCALLY COMPACT GROUPS
MONTGOMERY, D
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1948, 70 (02) : 327 - 332
[8] Locally compact quantum groups
Kustermans, Johan
[J]. QUANTUM INDEPENDENT INCREMENT PROCESSES I: FROM CLASSICAL PROBABILITY TO QUANTUM STOCHASTIC CALCULUS, 2005, 1865 : 99 - 180
[9] NORM OF LOCALLY COMPACT GROUPS
PERLT, E
STRAMBAC.K
[J]. ARCHIV DER MATHEMATIK, 1973, 24 : 355 - 365
[10] Locally compact Abelian groups
van Kampen, ER
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1934, 20 : 434 - 439

← 1 2 3 4 5 →