Commutators associated to a subfactor and its relative commutants  [ Commutateurs associés à un sous-facteur et à ses commutants relatifs ]
Annales de l'Institut Fourier, Tome 52 (2002) no. 1, p. 289-301
Soit NM une inclusion de facteurs de type II 1 ayant un indice de Jones fini. Alors on a l’égalité M=(N ' M)[N,M] en tant qu’espaces vectoriels. Ici [N,M] désigne l’espace vectoriel engendré par les commutateurs de la forme [a,b]aN,bM.
Let NM be an inclusion of II 1 factors with finite Jones index. Then M=(N ' M)[N,M] as a vector space. Here [N,M] denotes the vector space spanned by the commutators of the form [a,b] where aN,bM.
DOI : https://doi.org/10.5802/aif.1887
Classification:  46L37,  47B47
Mots clés: commutateur, attente conditionnelle, commutant relatif
@article{AIF_2002__52_1_289_0,
     author = {Huang, Hsiang-Ping},
     title = {Commutators associated to a subfactor and its relative commutants},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {52},
     number = {1},
     year = {2002},
     pages = {289-301},
     doi = {10.5802/aif.1887},
     zbl = {1021.46045},
     mrnumber = {1881581},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2002__52_1_289_0}
}
Huang, Hsiang-Ping. Commutators associated to a subfactor and its relative commutants. Annales de l'Institut Fourier, Tome 52 (2002) no. 1, pp. 289-301. doi : 10.5802/aif.1887. http://www.numdam.org/item/AIF_2002__52_1_289_0/

[1] D. Bisch Bimodules, higher relative commutants and the fusion algebra associated to a subfactor, Operator algebras and their applications (Waterloo, ON, 1994/1995), Amer. Math. Soc., Providence, RI (Fields Inst. Commun.) Tome 13 (1997), pp. 13-63 | Zbl 0894.46046

[2] M. Choda Entropy for canonical shifts, Trans. AMS, Tome 334 (1992) no. 2, pp. 827-849 | Article | MR 1070349 | Zbl 0773.46032

[3] D.E. Evans; Y. Kawahigashi Quantum symmetries on operator algebras, Oxford University Press, Oxford (1998) | MR 1642584 | Zbl 0924.46054

[4] Th. Fack; P. De La Harpe Sommes de commutateurs dans les algèbres de von Neumann finies continues, Ann. Inst. Fourier, Grenoble, Tome 30 (1980) no. 3, pp. 49-73 | Article | Numdam | MR 597017 | Zbl 0425.46046

[5] V.F.R. Jones Index for subrings of rings, Group actions on rings (Brunswick, Maine, 1984), Amer. Math. Soc., Providence, R.I. (Contemp. Math.) Tome 43 (1985), pp. 181-190 | Zbl 0607.46033

[6] V.F.R. Jones Planar algebras, I (1999) (preprint)

[7] S. Popa On a problem of R.V. Kadison on maximal abelian *-subalgebras in factors, Invent. Math., Tome 65 (1981), pp. 269-281 | Article | MR 641131 | Zbl 0481.46028

[8] S. Popa An axiomatization of the lattice of higher relative commutants of a subfactor, Invent. Math., Tome 120 (1995), pp. 427-445 | Article | MR 1334479 | Zbl 0831.46069

[9] S. Popa The relative Dixmier property for inclusions of von Neumann algebras of finite index, Ann. Sci. École Norm. Sup. (4), Tome 32 (1999) no. 6, pp. 743-767 | Numdam | MR 1717575 | Zbl 0966.46036

[10] S. Popa On the relative Dixmier property for inclusions of C*-algebras, J. Funct. Anal., Tome 171 (2000) no. 1, pp. 139-154 | Article | MR 1742862 | Zbl 0953.46027

[11] M. Takesaki Conditional expectations in von Neumann algebras, J. Func. Anal., Tome 9 (1972), pp. 306-321 | Article | MR 303307 | Zbl 0245.46089