Commutators associated to a subfactor and its relative commutants

Huang, Hsiang-Ping

doi:10.5802/aif.1887

Commutators associated to a subfactor and its relative commutants
[Commutateurs associés à un sous-facteur et à ses commutants relatifs]

Huang, Hsiang-Ping ¹

¹ University of California, Department of Mathematics, Los Angeles, CA 90095 (USA)

Annales de l'Institut Fourier, Tome 52 (2002) no. 1, pp. 289-301.

Résumé
Abstract

Soit $N \subseteq M$ une inclusion de facteurs de type $I I_{1}$ ayant un indice de Jones fini. Alors on a l’égalité $M = (N^{'} \cap M) \oplus [N, M]$ en tant qu’espaces vectoriels. Ici $[N, M]$ désigne l’espace vectoriel engendré par les commutateurs de la forme $[a, b]$ où $a \in N, b \in M$ .

Let $N \subseteq M$ be an inclusion of $I I_{1}$ factors with finite Jones index. Then $M = (N^{'} \cap M) \oplus [N, M]$ as a vector space. Here $[N, M]$ denotes the vector space spanned by the commutators of the form $[a, b]$ where $a \in N, b \in M$ .

MR Zbl

DOI : 10.5802/aif.1887

Classification : 46L37, 47B47
Keywords: commutator, conditional expectation, relative commutant
Mot clés : commutateur, attente conditionnelle, commutant relatif

Affiliations des auteurs :

Huang, Hsiang-Ping ¹

¹ University of California, Department of Mathematics, Los Angeles, CA 90095 (USA)

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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/articles/10.5802/aif.1887/

Bibliographie
Cité par

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

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

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

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

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

[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., Volume 65 (1981), pp. 269-281 | DOI | MR | Zbl

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

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

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

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

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