TY - JOUR
T1 - Non-microstates free entropy dimension for groups
AU - Mineyev, Igor
AU - Shlyakhtenko, Dimitri
N1 - Funding Information:
I.M.’s research partially supported by NSF CAREER grant DMS-0228910 and NSF grant DMS-0111298; the first author would also like to thank IAS, Princeton, for its hospitality in 2003-04. D.S.’s research supported by the Sloan Foundation and NSF Grant DMS-0102332.
PY - 2005/4
Y1 - 2005/4
N2 - 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.
AB - 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.
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U2 - 10.1007/s00039-005-0513-z
DO - 10.1007/s00039-005-0513-z
M3 - Article
AN - SCOPUS:23744503731
SN - 1016-443X
VL - 15
SP - 476
EP - 490
JO - Geometric and Functional Analysis
JF - Geometric and Functional Analysis
IS - 2
ER -