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)].


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


Zbl 0692.46049
Full Text: DOI EuDML


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