Rădulescu, Florin Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index. (English) Zbl 0861.46038 Invent. Math. 115, No. 2, 347-389 (1994). From the introduction: We introduce in this paper a noncommutative probability approach (in the sense considered by D. Voiculescu) to the algebras that are associated to certain amalgamated free products. In this way we find that the type \(\text{II}_1\) factors associated to the free, noncommutative groups \(F_N\), \(N\geq 2\) have a rich lattice of irreducible subfactors of noninteger index. Our main result states that many index values for irreducible subfactors of the hyperfinite \(\text{II}_1\) factor are also index values for irreducible subfactors of \({\mathcal L}(F_N)\). This answers a question raised by V. F. R. Jones [Operator algebras and applications, Vol. 2, Lond. Math. Soc., Lect. Notes Ser. 136, 103-118 (1988; Zbl 0692.46049)]. Reviewer: Kh.N.Boyadzhiev (Ada) Cited in 3 ReviewsCited in 88 Documents MSC: 46L37 Subfactors and their classification 46L51 Noncommutative measure and integration 46L53 Noncommutative probability and statistics 46L54 Free probability and free operator algebras 46L10 General theory of von Neumann algebras Keywords:noncommutative probability; amalgamated free products; type \(\text{II}_ 1\) factors; lattice of irreducible subfactors; hyperfinite \(\text{II}_ 1\) factor Citations:Zbl 0692.46049 PDF BibTeX XML Cite \textit{F. Rădulescu}, Invent. Math. 115, No. 2, 347--389 (1994; Zbl 0861.46038) Full Text: DOI EuDML References: [1] Anantharaman-Delaroche, C.: On Connes’ property T for von Neumann algebras. Math.-Japon.32, 337-355 (1987) · Zbl 0656.46052 [2] Boca, F.: On the method of constructing irreducible finite index subfactors of Popa. U.C.L.A., 1991 (Preprint) · Zbl 0795.46044 [3] Connes, A.: Un facteur du typeII 1 avec le groupe fondamentale denombrable. J. Oper. 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