Free Entropy Dimension in Amalgamated Free Products

Details Free Entropy Dimension in Amalgamated Free Products Free Entropy Dimension in Amalgamated Free Products

2006-09-04

arxiv.org/abs/math/0609080v5

Mathematics

Operator Algebras

The second revised version significantly generalized the main result of the original one, (see the abstract) and contains a ne

Scientific paper

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.

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