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Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index. (English) Zbl 0861.46038
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)].

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
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