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 CG, Voiculescu’s non-microstates free entropy dimension δ(X1, . . . , Xn) is exactly equal to β1(G) − β0(G) + 1, where βi are the L Betti numbers of G.

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Cite this paper

@inproceedings{Mineyev2005NonmicrostatesFE, title={Non-microstates Free Entropy Dimension for Groups}, author={Igor Mineyev}, year={2005} }