Non-microstates free entropy dimension for groups
Abstract
We show that for any discrete finitely-generated group G and any self-adjoint n-tuple X1,...,Xn of generators of the group algebra of G, Voiculescu's non-microstates free entropy dimension δ*(X1,...,Xn) is exactly equal to β1 (G)-β0 (G)+1, where βi are the L2 Betti numbers of G.
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