Geodesic
Multi-Sided Braid Type Subfactors, II
Canadian mathematical bulletin, Tome 46 (2003) no. 1, pp. 80-94

Voir la notice de l'article provenant de la source Cambridge University Press

We show that the multi-sided inclusion ${{R}^{\otimes l}}\,\subset \,R$ of braid-type subfactors of the hyperfinite $\text{I}{{\text{I}}_{1}}$ factor $R$ , introduced in Multi-sided braid type subfactors $[\text{E}3]$ , contains a sequence of intermediate subfactors: ${{R}^{\otimes l\,}}\subset \,{{R}^{\otimes l-1\,}}\subset \,\,\cdots \,\,\subset \,{{R}^{\otimes 2\,}}\subset \,R$ . That is, every $t$ -sided subfactor is an intermediate subfactor for the inclusion ${{R}^{\otimes l}}\,\subset \,R,\,\text{for 2}\,\le \,t\,\le \,l$ . Moreover, we also show that if $t\,>\,m$ then ${{R}^{\otimes t}}\,\subset \,{{R}^{\otimes m}}$ is conjugate to ${{R}^{\otimes t-m+1\,}}\subset \,R$ . Thus, if the braid representation considered is associated to one of the classical Lie algebras then the asymptotic inclusions for the Jones-Wenzl subfactors are intermediate subfactors.
DOI : 10.4153/CMB-2003-008-7
Mots-clés : 46L37 
Erlijman, Juliana. Multi-Sided Braid Type Subfactors, II. Canadian mathematical bulletin, Tome 46 (2003) no. 1, pp. 80-94. doi: 10.4153/CMB-2003-008-7
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[B] [B] Bisch, D., On the existence of central sequences in subfactors. Trans. Amer. Math. Soc. 321 (1989), 117–128. Google Scholar

[Bi] [Bi] Birman, J., Braids, links and mapping class groups. Ann.Math. Stud. 82, Princeton University Press, Princeton, NJ, 1974. Google Scholar

[Ch] [Ch] Choda, M., Index for factors generated by Jones’ two sided sequence of projections. Pacific J. Math 139 (1989), 1–16. Google Scholar

[E1] [E1] Erlijman, J., New braid subfactors from braid group representations. Trans. Amer.Math. Soc. 350 (1998), 185–211. Google Scholar

[E2] [E2] Erlijman, J., Two sided braid groups and asymptotic inclusions. Pacific J. Math 193 (2000), 57–78. Google Scholar

[E3] [E3] Erlijman, J., Multi-sided braid type subfactors. Canad. J. Math. (3) 53 (2001), 546–564. Google Scholar

[G] [G] Goto, S., Quantum double construction for subfactors arising from periodic commuting squares. J. Math. Soc. Japan 52 (2000), 187–198. Google Scholar

[Wa] [Wa] Wassermann, A., Operator algebras and conformal field theory. Proc. ICM Zürich, Birkäuser, 1994. Google Scholar

[W1] [W1] Wenzl, H., Hecke algebras of type An and subfactors. Invent.Math. 92 (1988), 349–383. Google Scholar

[W2] [W2] Wenzl, H., Quantum groups and subfactors of Lie type B, C, and D. Comm. Math. Phys. 133 (1990), 383–433. Google Scholar

[X] [X] Xu, F., Jones-Wassermann subfactors for disconnected intervals. Commun. Contemp.Math. 2 (2000), 307–347. Google Scholar

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