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Free entropy dimension in amalgamated free products
Author(s) -
Brown Nathanial P.,
Dykema Kenneth J.,
Jung Kenley
Publication year - 2008
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm054
Subject(s) - mathematics , free product , physics , quantum mechanics , group (periodic table)
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.