Geodesic
Multi-Sided Braid Type Subfactors
Canadian journal of mathematics, Tome 53 (2001) no. 3, pp. 546-564

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

We generalise the two-sided construction of examples of pairs of subfactors of the hyperfinite $\text{I}{{\text{I}}_{1}}$ factor $R$ in $[\text{E1}]$ —which arise by considering unitary braid representations with certain properties—to multi-sided pairs. We show that the index for the multi-sided pair can be expressed as a power of that for the two-sided pair. This construction can be applied to the natural examples—where the braid representations are obtained in connection with the representation theory of Lie algebras of types $A,\,B,\,C,\,D$ . We also compute the (first) relative commutants.
DOI : 10.4153/CJM-2001-023-8
Mots-clés : 46L37 
Erlijman, Juliana. Multi-Sided Braid Type Subfactors. Canadian journal of mathematics, Tome 53 (2001) no. 3, pp. 546-564. doi: 10.4153/CJM-2001-023-8
@article{10_4153_CJM_2001_023_8,
     author = {Erlijman, Juliana},
     title = {Multi-Sided {Braid} {Type} {Subfactors}},
     journal = {Canadian journal of mathematics},
     pages = {546--564},
     year = {2001},
     volume = {53},
     number = {3},
     doi = {10.4153/CJM-2001-023-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2001-023-8/}
}
TY  - JOUR
AU  - Erlijman, Juliana
TI  - Multi-Sided Braid Type Subfactors
JO  - Canadian journal of mathematics
PY  - 2001
SP  - 546
EP  - 564
VL  - 53
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2001-023-8/
DO  - 10.4153/CJM-2001-023-8
ID  - 10_4153_CJM_2001_023_8
ER  - 
%0 Journal Article
%A Erlijman, Juliana
%T Multi-Sided Braid Type Subfactors
%J Canadian journal of mathematics
%D 2001
%P 546-564
%V 53
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2001-023-8/
%R 10.4153/CJM-2001-023-8
%F 10_4153_CJM_2001_023_8

[B] [B] Birman, J., Braids, links and mapping class groups. Ann.Math. Studies 82, Princeton, New Jersey, Princeton Univ. Press. 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. (1) 193 (2000), 57–78. Google Scholar

[EK] [EK] Evans, D. and Kawahigashi, Y., Quantum symmetries on operator algebras. Oxford Mathematical Monographs, Oxford Science Publications, The Clarendon Press, Oxford University Press, 1998. Google Scholar

[G] [G] Goto, S., Quantum double construction for subfactors arising from periodic commuting squares. preprint, 1996. Google Scholar

[GHJ] [GHJ] Goodman, F., de la Harpe, P. and Jones, V., Coxeter graphs and towers of algebras. 14, Springer-Verlag, MSRI Publications, 1989. Google Scholar

[GW] [GW] Goodman, F. and Wenzl, H., Littlewood-Richardson coefficients for the Hecke algebra at roots of unity. Adv. inMath. 82 (1990), 24–45. Google Scholar

[O] [O] Ocneanu, A., Chirality of Operator Algebras. Subfactors, Taniguchi Symposium on Operator Algebras,World Scient. 1994, 39–63. Google Scholar

[P] [P] Popa, S., Orthogonal pairs of *-subalgebras of finite Von Neumann algebras. J. Operator Theory 9 (1983), 253–268. Google Scholar

[Wa] [Wa] Wassermann, A., Operator algebras and conformal field theory. Proc. ICMZürich, 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

[W4] [W4] Wenzl, H., Braids and invariants of 3-manifolds. Invent.Math. 114 (1993), 235–275. Google Scholar

[X] [X] Xu, F., Jones-Wassermann subfactors for disconnected intervals. preprint, QA/9704003. Google Scholar

Cité par Sources :