Non-microstates free entropy dimension for groups

Igor Mineyev, Dimitri Shlyakhtenko

Research output: Contribution to journalArticlepeer-review


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 ℓ2-Betti numbers of G.

Original languageEnglish (US)
Pages (from-to)476-490
Number of pages15
JournalGeometric and Functional Analysis
Issue number2
StatePublished - Apr 2005

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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