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Proceedings of the London Mathematical Society Advance Access published online on March 20, 2008
Proceedings of the London Mathematical Society, doi:10.1112/plms/pdm054
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© 2007 London Mathematical Society

Free entropy dimension in amalgamated free products

Nathanial P. Brown

Department of Mathematics
Penn State University
State College, PA 16802
USA

Kenneth J. Dykema

Department of Mathematics
Texas A&M University
College Station, TX 77843
USA
kdykema@math.tamu.edu

Kenley Jung

Department of Mathematics
University of California
Los Angeles
CA 90095
USA
kjung@math.ucla.edu

Received 31 October 2006. Revision received 31 August 2007.

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 L2-Betti number for certain amalgamated free products of groups is calculated.

2000 Mathematics Subject Classification 46L54 (46L35).


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