Non-microstates free entropy dimension for groups
Operator Algebras
2007-05-23 v2 Group Theory
Abstract
We show that for any discrete finitely-generated group G and any self-adjoint n-tuple X_1,...,X_n of generators of the group algebra of G, Voiculescu's non-microstates free entropy dimension \delta^*(X_1,...,X_n) is exactly equal to \beta_1 (G)-\beta_0 (G)+1, where \beta_i are the L^2 Betti numbers of G.
Cite
@article{arxiv.math/0312242,
title = {Non-microstates free entropy dimension for groups},
author = {I. Mineyev and D. Shlyakhtenko},
journal= {arXiv preprint arXiv:math/0312242},
year = {2007}
}
Comments
Revised version. Some explanations added and several typos fixed. To appear in Geom. and Func. Anal