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Non-microstates free entropy dimension for groups

I. Mineyev·D. Shlyakhtenko
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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 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.

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BibTeXRIS

I. Mineyev, D. Shlyakhtenko. 2005-02-01. Non-microstates free entropy dimension for groups. https://arxiv.org/abs/math/0312242

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