Bimodules, higher relative commutants, and the fusion algebra associated to a subfactor

1996 ◽  
pp. 13-63 ◽  
Author(s):  
Dietmar Bisch
Keyword(s):  
Fusion Algebra ◽  
Relative Commutants

scholarly journals Modular invariance and the fusion algebra

1988 ◽  
Vol 5 (2) ◽  
pp. 87-97 ◽  
Author(s):  
Robbert Dijkgraaf ◽  
Erik Verlinde
Keyword(s):  
Modular Invariance ◽  
Fusion Algebra

scholarly journals The Fusion Algebra of Bimodule Categories

2007 ◽  
Vol 16 (1-2) ◽  
pp. 123-140 ◽  
Author(s):  
Jürgen Fuchs ◽  
Ingo Runkel ◽  
Christoph Schweigert
Keyword(s):  
Fusion Algebra ◽  
Bimodule Categories

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

scholarly journals Affine Modules and the Drinfeld Center

2016 ◽  
Vol 118 (1) ◽  
pp. 119 ◽  
Author(s):  
Paramita Das ◽  
Shamindra Kumar Ghosh ◽  
Ved Prakash Gupta
Keyword(s):  
Finite Index ◽  
Planar Algebras ◽  
Infinite Depth ◽  
Zero Level ◽  
Fusion Algebra ◽  
Planar Algebra ◽  
The Way

Given a finite index subfactor, we show that the affine morphisms at zero level in the affine category over the planar algebra associated to the subfactor is isomorphic to the fusion algebra of the subfactor as a $*$-algebra. This identification paves the way to analyze the structure of affine $P$-modules with weight zero for any subfactor planar algebra $P$ (possibly having infinite depth). Further, for irreducible depth two subfactor planar algebras, we establish an additive equivalence between the category of affine $P$-modules and the center of the category of $N$-$N$-bimodules generated by $L^2(M)$; this partially verifies a conjecture of Jones and Walker.

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
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