Free entropy dimension in amalgamated free products

被引：35

作者：

Brown, Nathanial P. ^{[1
]}

Dykema, Kenneth J. ^{[2
]}

Jung, Kenley ^{[3
]}

机构：

[1] Penn State Univ, Dept Math, State Coll, PA 16802 USA

[2] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[3] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

来源：

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2008年 / 97卷

关键词：

D O I：

10.1112/plms/pdm054

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We calculate the microstates free entropy dimension of natural generators in an amalgamated free product of certain von Neumann algebras, with amalgamation over a hyperfinite subalgebra. In particular, some 'exotic' Popa algebra generators of free group factors are shown to have the expected free entropy dimension. We also show that microstates and non-microstates free entropy dimension agree for generating sets of many groups. In the appendix, the first L-2-Betti number for certain amalgamated free products of groups is calculated.

引用

页码：339 / 367

页数：29

共 32 条

[1] Group cohomology, harmonic functions and the first L-2-Betti number [J].

Bekka, MEB ;

Valette, A .

POTENTIAL ANALYSIS, 1997, 6 (04) :313-326

[2] Large deviation bounds for matrix Brownian motion [J].

Biane, P ;

Capitaine, M ;

Guionnet, A .

INVENTIONES MATHEMATICAE, 2003, 152 (02) :433-459

[3]

Brown NP, 2004, J REINE ANGEW MATH, V573, P157

[4]

BROWN NP, 2006, MEM AM MATH SOC, V184

[5] L2-COHOMOLOGY AND GROUP COHOMOLOGY [J].

CHEEGER, J ;

GROMOV, M .

TOPOLOGY, 1986, 25 (02) :189-215

[6]

Connes A, 2005, J REINE ANGEW MATH, V586, P125

[7]

DICKS W, 2005, ARXIVMATH0508370

[8] INTERPOLATED FREE GROUP FACTORS [J].

DYKEMA, K .

PACIFIC JOURNAL OF MATHEMATICS, 1994, 163 (01) :123-135

[9]

Dykema K, 2005, DOC MATH, V10, P247

[10] FREE-PRODUCTS OF HYPERFINITE VON NEUMANN ALGEBRAS AND FREE DIMENSION [J].

DYKEMA, K .

DUKE MATHEMATICAL JOURNAL, 1993, 69 (01) :97-119

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