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Non-microstates free entropy dimension for groups

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Geometric & Functional Analysis GAFA Aims and scope Submit manuscript

Abstract.

We show that for any discrete finitely-generated group G and any self-adjoint n-tuple X1,...,X n of generators of the group algebra \(\mathbb{C}G,\) Voiculescu’s non-microstates free entropy dimension δ*(X1,...,X n ) is exactly equal to β1(G) − β0(G) + 1 where β i are the ℓ2-Betti numbers of G.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 250 Altgeld Hall, 1409 West Green St, Urbana, IL, 61801, USA

    I. Mineyev

  2. Department of Mathematics, UCLA, Los Angeles, CA, 90095, USA

    D. Shlyakhtenko

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  1. I. Mineyev
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  2. D. Shlyakhtenko
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Correspondence to I. Mineyev.

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Received: January 2004 Revision: October 2004 Accepted: January 2005

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Mineyev, I., Shlyakhtenko, D. Non-microstates free entropy dimension for groups. GAFA, Geom. funct. anal. 15, 476–490 (2005). https://doi.org/10.1007/s00039-005-0513-z

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  • DOI: https://doi.org/10.1007/s00039-005-0513-z

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