Non-microstates free entropy dimension for groups

Details Non-microstates free entropy dimension for groups Non-microstates free entropy dimension for groups

2003-12-11

arxiv.org/abs/math/0312242v2

Mathematics

Operator Algebras

Revised version. Some explanations added and several typos fixed. To appear in Geom. and Func. Anal

Scientific paper

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.

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