Irreducible subfactors of $L(\mathbb F_\infty)$ of index $λ>4$

Details Irreducible subfactors of $L(\mathbb F_\infty)$ of index $λ>4$ Irreducible subfactors of $L(\mathbb F_\infty)$ of index $λ>4$

2000-10-20

arxiv.org/abs/math/0010202v2

Mathematics

Operator Algebras

Final version (correcting typos and adding an appendix)

Scientific paper

By utilizing an irreducible inclusion of type III$_{q^{2}} $ factors coming from a free-product type action of the quantum group $ SU_{q}(2) $, we show that the free group factor $ L(\mathbb {F}_{\infty}) $ possesses irreducible subfactors of arbitrary index $ >4 $. Combined with earlier results of Radulescu, this shows that $ L(\mathbb {F}_{\infty}) $ has irreducible subfactors with any index value in $ \{4\cos ^{2}(\pi /n):n\geq 3\}\cup [4,+\infty) $.

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