Compact actions and uniqueness of the group measure space decomposition of II1 factors

被引：5
作者：
Ioana, Adrian [1 ]
机构：
[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 262卷 / 10期
关键词：
II1; factor; Group measure space construction; Cartan subalgebra; Compact action; MALLEABLE ACTIONS; SUPERRIGIDITY;
D O I：
10.1016/j.jfa.2012.03.004
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
preserving action of a countable group Gamma with positive first l(2)-Betti number, beta((2))(1) (Gamma) > 0, has a uniqueWe prove that any II1 factor L-infinity (X) x Gamma arising from a compact, free, ergodic, probability measure group measure space Cartan subalgebra, up to unitary conjugacy. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：4525 / 4533
页数：9
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[21]   Examples of property (T) II1 factors with trivial fundamental group [J].
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Das, Sayan ;
Houdayer, Cyril ;
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AMERICAN JOURNAL OF MATHEMATICS, 2024, 146 (02) :435-465
[22]   Construction of type II1 factors with prescribed countable fundamental group [J].
Houdayer, Cyril .
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2009, 634 :169-207
[23]   Primeness of generalized wreath product II1 factors [J].
Patchell, Gregory .
MATHEMATISCHE ZEITSCHRIFT, 2025, 309 (03)
[24]   Existentially closed II1 factors [J].
Farah, Ilijas ;
Goldbring, Isaac ;
Hart, Bradd ;
Sherman, David .
FUNDAMENTA MATHEMATICAE, 2016, 233 (02) :173-196
[25]   W*-Rigidity Paradigms for Embeddings of II1 Factors [J].
Popa, Sorin ;
Vaes, Stefaan .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2022, 395 (02) :907-961
[26]   Notes on automorphisms of ultrapowers of II1 factors [J].
Sherman, David .
STUDIA MATHEMATICA, 2009, 195 (03) :201-217
[27]   UNBOUNDED DERIVATIONS, FREE DILATIONS, AND INDECOMPOSABILITY RESULTS FOR II1 FACTORS [J].
Dabrowski, Yoann ;
Ioana, Adrian .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 368 (07) :4525-4560
[28]   Strongly Solid II1 Factors with an Exotic MASA [J].
Houdayer, Cyril ;
Shlyakhtenko, Dimitri .
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2011, 2011 (06) :1352-1380
[29]   Embedding universality for II1 factors with property (T) [J].
Chifan, Ionut ;
Drimbe, Daniel ;
Ioana, Adrian .
ADVANCES IN MATHEMATICS, 2023, 417
[30]   Existential closedness and the structure of bimodules of II1 factors [J].
Ioana, Adrian ;
Tan, Hui .
JOURNAL OF FUNCTIONAL ANALYSIS, 2024, 286 (04)
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