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

Dimitri Shlyakhtenko·Yoshimichi Ueda
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Abstract

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}(π/n):n\geq 3\}\cup [4,+\infty) $.

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Dimitri Shlyakhtenko, Yoshimichi Ueda. 2001-06-29. Irreducible subfactors of $L(\mathbb F_\infty)$ of index $λ>4$. https://arxiv.org/abs/math/0010202

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