Free Entropy Dimension in Amalgamated Free Products

Abstract

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 by Wolfgang Lueck, the first L^2-Betti number for certain amalgamated free products of groups is calculated.

The second revised version significantly generalized the main result of the original one, (see the abstract) and contains a new appendix by Wolfgang Lueck. The third and fourth revisions correct some minor mistakes. The fifth version adds a result about embeddability of amalgmated free products

References in corpus (3)

• Invariant means and finite representation theory of C*-algebras
• L^2-Homology for von Neumann Algebras
• All generating sets of all property T von Neumann algebras have free entropy dimension $\le 1$

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