Free entropy dimension in amalgamated free products

Nathanial P. Brown; Kenneth J. Dykema; Kenley Jung; Wolfgang Lück

doi:10.1112/plms/pdm054

Free entropy dimension in amalgamated free products

Nathanial P. Brown, Kenneth J. Dykema, Kenley Jung, Wolfgang Lück

Mathematics

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

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

Original language	English (US)
Pages (from-to)	339-367
Number of pages	29
Journal	Proceedings of the London Mathematical Society
Volume	97
Issue number	2
DOIs	https://doi.org/10.1112/plms/pdm054
State	Published - Sep 2008

All Science Journal Classification (ASJC) codes

General Mathematics

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title = "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, the first L2-Betti number for certain amalgamated free products of groups is calculated.",

author = "Brown, {Nathanial P.} and Dykema, {Kenneth J.} and Kenley Jung and Wolfgang L{\"u}ck",

note = "Funding Information: N.B. partially supported by NSF grant DMS-0244807/0554870, K.D. by DMS-0300336/ 0600814 and K.J. by graduate and postdoctoral NSF fellowships.",

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AU - Brown, Nathanial P.

AU - Dykema, Kenneth J.

AU - Jung, Kenley

AU - Lück, Wolfgang

N1 - Funding Information: N.B. partially supported by NSF grant DMS-0244807/0554870, K.D. by DMS-0300336/ 0600814 and K.J. by graduate and postdoctoral NSF fellowships.

PY - 2008/9

Y1 - 2008/9

N2 - 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.

AB - 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.

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Free entropy dimension in amalgamated free products

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