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

Dimitri Shlyakhtenko; Yoshimichi Ueda

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

Operator Algebras 2007-05-23 v2

Authors: Dimitri Shlyakhtenko , Yoshimichi Ueda

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 $\{4\cos ^{2}(\pi /n):n\geq 3\}\cup [4,+\infty)$ .

Keywords

free group factors irreducible subfactors index quantum group su_q(2) type iii factors free-product action

Cite

@article{arxiv.math/0010202,
  title  = {Irreducible subfactors of $L(\mathbb F_\infty)$ of index $\lambda>4$},
  author = {Dimitri Shlyakhtenko and Yoshimichi Ueda},
  journal= {arXiv preprint arXiv:math/0010202},
  year   = {2007}
}

Comments

Final version (correcting typos and adding an appendix)

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

Abstract

Keywords

Cite

Comments

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