Commutators associated to a subfactor and its relative commutants
- [1] University of California, Department of Mathematics, Los Angeles, CA 90095 (USA)
Annales de l’institut Fourier (2002)
- Volume: 52, Issue: 1, page 289-301
- ISSN: 0373-0956
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topHuang, Hsiang-Ping. "Commutators associated to a subfactor and its relative commutants." Annales de l’institut Fourier 52.1 (2002): 289-301. <http://eudml.org/doc/115978>.
@article{Huang2002,
abstract = {Let $N\subseteq M$ be an inclusion of $II_1$ factors with finite Jones index. Then $M =
\{(N^\{\prime \} \cap M)\} \oplus [N, M]$ as a vector space. Here $[N, M]$ denotes the vector space
spanned by the commutators of the form $[a, b]$ where $a \in N,\, b \in M$.},
affiliation = {University of California, Department of Mathematics, Los Angeles, CA 90095 (USA)},
author = {Huang, Hsiang-Ping},
journal = {Annales de l’institut Fourier},
keywords = {commutator; conditional expectation; relative commutant; subfactor; cyclic tensor product},
language = {eng},
number = {1},
pages = {289-301},
publisher = {Association des Annales de l'Institut Fourier},
title = {Commutators associated to a subfactor and its relative commutants},
url = {http://eudml.org/doc/115978},
volume = {52},
year = {2002},
}
TY - JOUR
AU - Huang, Hsiang-Ping
TI - Commutators associated to a subfactor and its relative commutants
JO - Annales de l’institut Fourier
PY - 2002
PB - Association des Annales de l'Institut Fourier
VL - 52
IS - 1
SP - 289
EP - 301
AB - Let $N\subseteq M$ be an inclusion of $II_1$ factors with finite Jones index. Then $M =
{(N^{\prime } \cap M)} \oplus [N, M]$ as a vector space. Here $[N, M]$ denotes the vector space
spanned by the commutators of the form $[a, b]$ where $a \in N,\, b \in M$.
LA - eng
KW - commutator; conditional expectation; relative commutant; subfactor; cyclic tensor product
UR - http://eudml.org/doc/115978
ER -
References
top- D. Bisch, Bimodules, higher relative commutants and the fusion algebra associated to a subfactor, Operator algebras and their applications (Waterloo, ON, 1994/1995) 13 (1997), 13-63, Amer. Math. Soc., Providence, RI Zbl0894.46046
- M. Choda, Entropy for canonical shifts, Trans. AMS 334 (1992), 827-849 Zbl0773.46032MR1070349
- D.E. Evans, Y. Kawahigashi, Quantum symmetries on operator algebras, (1998), Oxford University Press, Oxford Zbl0924.46054MR1642584
- Th. Fack, P. de la Harpe, Sommes de commutateurs dans les algèbres de von Neumann finies continues, Ann. Inst. Fourier, Grenoble 30 (1980), 49-73 Zbl0425.46046MR597017
- V.F.R. Jones, Index for subrings of rings, Group actions on rings (Brunswick, Maine, 1984) 43 (1985), 181-190, Amer. Math. Soc., Providence, R.I. Zbl0607.46033
- V.F.R. Jones, Planar algebras, I, (1999)
- S. Popa, On a problem of R.V. Kadison on maximal abelian *-subalgebras in factors, Invent. Math. 65 (1981), 269-281 Zbl0481.46028MR641131
- S. Popa, An axiomatization of the lattice of higher relative commutants of a subfactor, Invent. Math. 120 (1995), 427-445 Zbl0831.46069MR1334479
- S. Popa, The relative Dixmier property for inclusions of von Neumann algebras of finite index, Ann. Sci. École Norm. Sup. (4) 32 (1999), 743-767 Zbl0966.46036MR1717575
- S. Popa, On the relative Dixmier property for inclusions of C*-algebras, J. Funct. Anal. 171 (2000), 139-154 Zbl0953.46027MR1742862
- M. Takesaki, Conditional expectations in von Neumann algebras, J. Func. Anal. 9 (1972), 306-321 Zbl0245.46089MR303307
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