Non-microstates free entropy dimension for groups
Abstract
Description
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 δ^*(X_1,...,X_n) is exactly equal to β_1 (G)-β_0 (G)+1, where β_i are the L^2 Betti numbers of G.
Revised version. Some explanations added and several typos fixed. To appear in Geom. and Func. Anal
Revised version. Some explanations added and several typos fixed. To appear in Geom. and Func. Anal