Commutators associated to a subfactor and its relative commutants

2002 ◽  
Vol 52 (1) ◽  
pp. 289-301 ◽  
Author(s):  
Hsiang-Ping Huang
Keyword(s):  
Relative Commutants

scholarly journals LOCAL NATURE OF COSET MODELS

2004 ◽  
Vol 16 (03) ◽  
pp. 353-382 ◽  
Author(s):  
S. KÖSTER
Keyword(s):  
Representation Formula ◽  
Adjoint Action ◽  
Energy Tensor ◽  
Local Algebras ◽  
Relative Commutants ◽  
Stress Energy ◽  
Local Observables ◽  
Coset Models ◽  
Geometric Picture ◽  
Local Nature

The local algebras of the maximal Coset model [Formula: see text] associated with a chiral conformal subtheory [Formula: see text] are shown to coincide with the local relative commutants of [Formula: see text] in ℬ, provided [Formula: see text] possesses a stress-energy tensor.Making the same assumption, the adjoint action of the unique inner-implementing representation [Formula: see text] associated with [Formula: see text] on the local observables in ℬ is found to define net-endomorphisms of ℬ. This property is exploited for constructing from ℬ a conformally covariant holographic image in (1+1) dimensions which proves useful as a geometric picture for the joint inclusion [Formula: see text].Immediate applications to the analysis of current subalgebras are given and the relation to normal canonical tensor product subfactors is clarified. A natural converse of Borchers' theorem on half-sided translations is made accessible.

scholarly journals On the relative commutants of subfactors

1998 ◽  
Vol 126 (9) ◽  
pp. 2725-2732
Author(s):  
M. Khoshkam ◽  
B. Mashood
Keyword(s):  
Relative Commutants

Multi-Sided Braid Type Subfactors

2001 ◽  
Vol 53 (3) ◽  
pp. 546-564 ◽  
Author(s):  
Juliana Erlijman
Keyword(s):  
Representation Theory ◽  
Lie Algebras ◽  
Relative Commutants

AbstractWe generalise the two-sided construction of examples of pairs of subfactors of the hyperfinite II1 factor R in [E1]—which arise by considering unitary braid representations with certain properties—to multisided 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.

scholarly journals Relative commutants of strongly self-absorbing $$\mathrm {C}^*$$ C ∗ -algebras

2016 ◽  
Vol 23 (1) ◽  
pp. 363-387 ◽  
Author(s):  
Ilijas Farah ◽  
Bradd Hart ◽  
Mikael Rørdam ◽  
Aaron Tikuisis
Keyword(s):  
C Algebras ◽  
Relative Commutants

On relative commutants in tensor products ofC *-algebras

1976 ◽  
Vol 151 (3) ◽  
pp. 215-218 ◽  
Author(s):  
Charles J. K. Batty
Keyword(s):  
Tensor Products ◽  
Relative Commutants

scholarly journals Factorial relative commutants and the generalized Jung property for II1 factors

2021 ◽  
pp. 108107
Author(s):  
Scott Atkinson ◽  
Isaac Goldbring ◽  
Srivatsav Kunnawalkam Elayavalli
Keyword(s):  
Relative Commutants
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